Professor Mark Powell

  • Professor of Mathematics (Mathematics)

Biography

Research interests

Algebraic and geometric topology, and homological algebra. I specialise in the topology of manifolds, especially in dimensions 3 and 4.

Research groups

Publications

List by: Type | Date

Jump to: 2024 | 2023 | 2022 | 2021 | 2020 | 2019 | 2018 | 2017 | 2016 | 2014 | 2012
Number of items: 54.

2024

Conway, A., Crowley, D., Powell, M. and Sixt, J. (2024) Stably diffeomorphic manifolds and the realisation of modified surgery obstructions = Variétés stablement difféomorphes et la réalisation des obstructions en théorie de la chirurgie modifiée. Memoires de la Société Mathématique de France, (Accepted for Publication)

Juhasz, A. and Powell, M. (2024) Examples of topologically unknotted tori. Transactions of the American Mathematical Society, (Accepted for Publication)

Kasprowski, D., Powell, M. and Ruppik, B. (2024) Homotopy classification of 4-manifolds with finite abelian 2-generator fundamental groups. Mathematical Proceedings of the Cambridge Philosophical Society, (Accepted for Publication)

Friedl, S., Nagel, M., Orson, P. and Powell, M. (2024) The foundations of four-manifold theory in the topological category. New York Journal of Mathematics, (Accepted for Publication)

Orson, P. and Powell, M. (2024) Simple spines of homotopy 2-spheres are unique. Proceedings of the London Mathematical Society, 128(2), e12583. (doi: 10.1112/plms.12583)

2023

Conway, A., Crowley, D. and Powell, M. (2023) Infinite homotopy stable class for 4-manifolds with boundary. Pacific Journal of Mathematics, 325(2), pp. 209-237. (doi: 10.2140/pjm.2023.325.209)

Hayden, K., Kjuchukova, A., Krishna, S., Miller, M., Powell, M. and Sunukjian, N. (2023) Brunnian exotic surface links in the 4-ball. Michigan Mathematical Journal, (Accepted for Publication)

Kasprowski, D., Powell, M. and Teichner, P. (2023) Algebraic criteria for stable diffeomorphism of spin 4-manifolds. Memoirs of the American Mathematical Society, (Accepted for Publication)

Miller, A. N. and Powell, M. (2023) Strongly invertible knots, equivariant slice genera, and an equivariant algebraic concordance group. Journal of the London Mathematical Society, 107(6), pp. 2025-2053. (doi: 10.1112/jlms.12732)

Conway, A. and Powell, M. (2023) Embedded surfaces with infinite cyclic knot group. Geometry and Topology, 27(2), pp. 739-821. (doi: 10.2140/gt.2023.27.739)

Kasprowski, D., Powell, M. , Ray, A. and Teichner, P. (2023) Embedding surfaces in 4-manifolds. Geometry and Topology, (Accepted for Publication)

Kasprowski, D., Powell, M. and Ray, A. (2023) Gluck twists on concordant or homotopic spheres. Mathematical Research Letters, (Accepted for Publication)

Kasprowski, D., Powell, M. and Ray, A. (2023) Counterexamples in 4-manifold topology. EMS Surveys in Mathematical Sciences, 9(1), pp. 193-249. (doi: 10.4171/EMSS/56)

Feller, P., Park, J. and Powell, M. (2023) The Z-genus of boundary links. Revista Matemática Complutense, 36(1), pp. 1-25. (doi: 10.1007/s13163-022-00424-3)

2022

Orson, P. and Powell, M. (2022) Doubly slice knots and metabelian obstructions. Journal of Topology and Analysis, 14(4), pp. 847-873. (doi: 10.1142/S1793525321500229)

Park, J. and Powell, M. (2022) A ribbon obstruction and derivatives of knots. Israel Journal of Mathematics, 250(1), pp. 265-305. (doi: 10.1007/s11856-022-2338-y)

Conway, A., Crowley, D., Powell, M. and Sixt, J. (2022) Simply connected manifolds with large homotopy stable classes. Journal of the Australian Mathematical Society, (doi: 10.1017/S1446788722000167) (Early Online Publication)

Friedl, S., Kitayama, T., Lewark, L., Nagel, M. and Powell, M. (2022) Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials. Canadian Journal of Mathematics, 74(4), pp. 1137-1176. (doi: 10.4153/S0008414X21000183)

Kasprowski, D., Powell, M. and Teichner, P. (2022) Four-manifolds up to connected sum with complex projective planes. American Journal of Mathematics, 144(1), pp. 75-118. (doi: 10.1353/ajm.2022.0001)

2021

Conway, A. and Powell, M. (2021) Characterisation of homotopy ribbon discs. Advances in Mathematics, 391, 107960. (doi: 10.1016/j.aim.2021.107960)

Behrens, S., Kalmar, B., Kim, M. H., Powell, M. and Ray, A. (Eds.) (2021) The Disc Embedding Theorem. Oxford University Press: Oxford. ISBN 9780198841319

Orson, P. and Powell, M. (2021) A lower bound for the doubly slice genus from signatures. New York Journal of Mathematics, 27, pp. 379-392.

Cha, J. C., Miller, A. N. and Powell, M. (2021) Two-solvable and two-bipolar knots with large four-genera. Mathematical Research Letters, 28(2), pp. 331-382. (doi: 10.4310/MRL.2021.v28.n2.a2)

Feller, P., Miller, A. N., Nagel, M., Orson, P., Powell, M. and Ray, A. (2021) Embedding spheres in knot traces. Compositio Mathematica, 157(10), pp. 2242-2279. (doi: 10.1112/s0010437x21007508)

Kim, M. H., Powell, M. and Teichner, P. (2021) Round handle problem. Pure and Applied Mathematics Quarterly, 17(1), pp. 237-347. (doi: 10.4310/PAMQ.2021.v17.n1.a6)

2020

Friedl, S. and Powell, M. (2020) Homotopy ribbon concordance and Alexander polynomials. Archiv der Mathematik, 115(6), pp. 717-725. (doi: 10.1007/s00013-020-01517-5)

Cha, J. C., Kim, M. H. and Powell, M. (2020) A family of freely slice good boundary links. Mathematische Annalen, 376(3-4), pp. 1009-1030. (doi: 10.1007/s00208-019-01907-3)

Cha, J. C., Orr, K. E. and Powell, M. (2020) Whitney towers and abelian invariants of knots. Mathematische Zeitschrift, 294(1-2), pp. 519-553. (doi: 10.1007/s00209-019-02293-x)

Davis, C. W., Nagel, M., Orson, P. and Powell, M. (2020) Surface systems and triple linking numbers. Indiana University Mathematics Journal, 69(7), pp. 2505-2547. (doi: 10.1512/iumj.2020.69.8081)

2019

Nagel, M., Orson, P., Park, J. and Powell, M. (2019) Smooth and topological almost concordance. International Mathematics Research Notices, 2019(23), pp. 7324-7355. (doi: 10.1093/imrn/rnx338)

Friedl, S., Nagel, M., Orson, P. and Powell, M. (2019) Satellites and concordance of knots in 3–manifolds. Transactions of the American Mathematical Society, 371(4), pp. 2279-2306. (doi: 10.1090/tran/7313)

Miller, A. N. and Powell, M. (2019) Stabilization distance between surfaces. L’Enseignement Mathématique, 65(3/4), pp. 397-440. (doi: 10.4171/lem/65-3/4-4)

2018

Miller, A. N. and Powell, M. (2018) Symmetric chain complexes, twisted Blanchfield pairings and knot concordance. Algebraic and Geometric Topology, 18(6), pp. 3425-2476. (doi: 10.2140/agt.2018.18.3425)

2017

Nagel, M. and Powell, M. (2017) Concordance invariance of Levine-Tristram signatures of links. Documenta Mathematica, 22, pp. 25-43. (doi: 10.25537/dm.2017v22.25-43)

Kasprowski, D., Land, M., Powell, M. and Teichner, P. (2017) Stable classification of 4-manifolds with 3-manifold fundamental groups. Journal of Topology, 10(3), pp. 827-881. (doi: 10.1112/topo.12025)

Powell, M. , Cochran, T. D. and Harvey, S. (2017) Grope metrics on the knot concordance set. Journal of Topology, 10(3), pp. 669-699. (doi: 10.1112/topo.12018)

Cha, J. C., Friedl, S. and Powell, M. (2017) Splitting numbers of links. Proceedings of the Edinburgh Mathematical Society, 60(3), pp. 587-614. (doi: 10.1017/S0013091516000420)

Powell, M. (2017) The four-genus of a link, Levine–Tristram signatures and satellites. Journal of Knot Theory and Its Ramifications, 26(2), 1740008. (doi: 10.1142/s0218216517400089)

Friedl, S. and Powell, M. (2017) A calculation of Blanchfield pairings of 3-manifolds and knots. Moscow Mathematical Journal, 17(1), pp. 59-77. (doi: 10.17323/1609-4514-2017-17-1-59-77)

Fruedk, S., Leidy, C., Nagel, M. and Powell, M. (2017) Twisted Blanchfield pairings and decompositions of 3-manifolds. Homology, Homotopy and Applications, 19(2), pp. 275-287. (doi: 10.4310/HHA.2017.v19.n2.a14)

2016

Powell, M. (2016) Twisted Blanchfield pairings and symmetric chain complexes. Quarterly Journal of Mathematics, 67(4), pp. 715-742. (doi: 10.1093/qmath/haw028)

Cha, J. C. and Powell, M. (2016) Casson towers and slice links. Inventiones Mathematicae, 205(2), pp. 413-457. (doi: 10.1007/s00222-015-0639-z)

Borodzik, M., Friedl, S. and Powell, M. (2016) Blanchfield forms and Gordian distance. Journal of the Mathematical Society of Japan, 68(3), pp. 1047-1080. (doi: 10.2969/jmsj/06831047)

Borodzik, M. and Powell, M. (2016) Embedded Morse theory and relative splitting of cobordisms of manifolds. Journal of Geometric Analysis, 26(1), pp. 57-87. (doi: 10.1007/s12220-014-9538-6)

2014

Friedl, S., Nagel, M. and Powell, M. (2014) A specious unlinking strategy. Periodica Mathematica Hungarica, 69(2), pp. 207-210. (doi: 10.1007/s10998-014-0063-y)

Cha, J. C., Friedl, S. and Powell, M. (2014) Concordance of links with identical Alexander invariants. Bulletin of the London Mathematical Society, 46(3), pp. 629-642. (doi: 10.1112/blms/bdu002)

Friedl, S. and Powell, M. (2014) Links not concordant to the Hopf link. Mathematical Proceedings of the Cambridge Philosophical Society, 156(3), pp. 425-459. (doi: 10.1017/S0305004114000036)

Friedl, S. and Powell, M. (2014) Cobordisms to weakly splittable links. Proceedings of the American Mathematical Society, 142(2), pp. 703-712. (doi: 10.1090/S0002-9939-2013-11792-2)

Cha, J. C. and Powell, M. (2014) Covering link calculus and the bipolar filtration of topologically slice links. Geometry and Topology, 18(3), pp. 1539-1579. (doi: 10.2140/gt.2014.18.1539)

Cha, J. C. and Powell, M. (2014) Nonconcordant links with homology cobordant zero-framed surgery manifolds. Pacific Journal of Mathematics, 272(1), pp. 1-33. (doi: 10.2140/PJM.2014.272.1)

Kasprowski, D. and Powell, M. (2014) Shrinking of toroidal decomposition spaces. Fundamenta Mathematicae, 227, pp. 271-296. (doi: 10.4064/fm227-3-3)

2012

Friedl, S. and Powell, M. (2012) An injectivity theorem for Casson-Gordon type representations relating to the concordance of knots and links. Bulletin of the Korean Mathematical Society, 49(2), pp. 395-409. (doi: 10.4134/BKMS.2012.49.2.395)

Balm, C., Friedl, S., Kalfagianni, E. and Powell, M. (2012) Cosmetic crossings and Seifert matrices. Communications in Analysis and Geometry, 20(2), pp. 235-253. (doi: 10.4310/CAG.2012.v20.n2.a1)

Powell, M. (2012) A second order algebraic knot concordance group. Algebraic and Geometric Topology, 12(2), pp. 685-751. (doi: 10.2140/agt.2012.12.685)

This list was generated on Sun Jul 21 22:07:16 2024 BST.
Number of items: 54.

Articles

Conway, A., Crowley, D., Powell, M. and Sixt, J. (2024) Stably diffeomorphic manifolds and the realisation of modified surgery obstructions = Variétés stablement difféomorphes et la réalisation des obstructions en théorie de la chirurgie modifiée. Memoires de la Société Mathématique de France, (Accepted for Publication)

Juhasz, A. and Powell, M. (2024) Examples of topologically unknotted tori. Transactions of the American Mathematical Society, (Accepted for Publication)

Kasprowski, D., Powell, M. and Ruppik, B. (2024) Homotopy classification of 4-manifolds with finite abelian 2-generator fundamental groups. Mathematical Proceedings of the Cambridge Philosophical Society, (Accepted for Publication)

Friedl, S., Nagel, M., Orson, P. and Powell, M. (2024) The foundations of four-manifold theory in the topological category. New York Journal of Mathematics, (Accepted for Publication)

Orson, P. and Powell, M. (2024) Simple spines of homotopy 2-spheres are unique. Proceedings of the London Mathematical Society, 128(2), e12583. (doi: 10.1112/plms.12583)

Conway, A., Crowley, D. and Powell, M. (2023) Infinite homotopy stable class for 4-manifolds with boundary. Pacific Journal of Mathematics, 325(2), pp. 209-237. (doi: 10.2140/pjm.2023.325.209)

Hayden, K., Kjuchukova, A., Krishna, S., Miller, M., Powell, M. and Sunukjian, N. (2023) Brunnian exotic surface links in the 4-ball. Michigan Mathematical Journal, (Accepted for Publication)

Kasprowski, D., Powell, M. and Teichner, P. (2023) Algebraic criteria for stable diffeomorphism of spin 4-manifolds. Memoirs of the American Mathematical Society, (Accepted for Publication)

Miller, A. N. and Powell, M. (2023) Strongly invertible knots, equivariant slice genera, and an equivariant algebraic concordance group. Journal of the London Mathematical Society, 107(6), pp. 2025-2053. (doi: 10.1112/jlms.12732)

Conway, A. and Powell, M. (2023) Embedded surfaces with infinite cyclic knot group. Geometry and Topology, 27(2), pp. 739-821. (doi: 10.2140/gt.2023.27.739)

Kasprowski, D., Powell, M. , Ray, A. and Teichner, P. (2023) Embedding surfaces in 4-manifolds. Geometry and Topology, (Accepted for Publication)

Kasprowski, D., Powell, M. and Ray, A. (2023) Gluck twists on concordant or homotopic spheres. Mathematical Research Letters, (Accepted for Publication)

Kasprowski, D., Powell, M. and Ray, A. (2023) Counterexamples in 4-manifold topology. EMS Surveys in Mathematical Sciences, 9(1), pp. 193-249. (doi: 10.4171/EMSS/56)

Feller, P., Park, J. and Powell, M. (2023) The Z-genus of boundary links. Revista Matemática Complutense, 36(1), pp. 1-25. (doi: 10.1007/s13163-022-00424-3)

Orson, P. and Powell, M. (2022) Doubly slice knots and metabelian obstructions. Journal of Topology and Analysis, 14(4), pp. 847-873. (doi: 10.1142/S1793525321500229)

Park, J. and Powell, M. (2022) A ribbon obstruction and derivatives of knots. Israel Journal of Mathematics, 250(1), pp. 265-305. (doi: 10.1007/s11856-022-2338-y)

Conway, A., Crowley, D., Powell, M. and Sixt, J. (2022) Simply connected manifolds with large homotopy stable classes. Journal of the Australian Mathematical Society, (doi: 10.1017/S1446788722000167) (Early Online Publication)

Friedl, S., Kitayama, T., Lewark, L., Nagel, M. and Powell, M. (2022) Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials. Canadian Journal of Mathematics, 74(4), pp. 1137-1176. (doi: 10.4153/S0008414X21000183)

Kasprowski, D., Powell, M. and Teichner, P. (2022) Four-manifolds up to connected sum with complex projective planes. American Journal of Mathematics, 144(1), pp. 75-118. (doi: 10.1353/ajm.2022.0001)

Conway, A. and Powell, M. (2021) Characterisation of homotopy ribbon discs. Advances in Mathematics, 391, 107960. (doi: 10.1016/j.aim.2021.107960)

Orson, P. and Powell, M. (2021) A lower bound for the doubly slice genus from signatures. New York Journal of Mathematics, 27, pp. 379-392.

Cha, J. C., Miller, A. N. and Powell, M. (2021) Two-solvable and two-bipolar knots with large four-genera. Mathematical Research Letters, 28(2), pp. 331-382. (doi: 10.4310/MRL.2021.v28.n2.a2)

Feller, P., Miller, A. N., Nagel, M., Orson, P., Powell, M. and Ray, A. (2021) Embedding spheres in knot traces. Compositio Mathematica, 157(10), pp. 2242-2279. (doi: 10.1112/s0010437x21007508)

Kim, M. H., Powell, M. and Teichner, P. (2021) Round handle problem. Pure and Applied Mathematics Quarterly, 17(1), pp. 237-347. (doi: 10.4310/PAMQ.2021.v17.n1.a6)

Friedl, S. and Powell, M. (2020) Homotopy ribbon concordance and Alexander polynomials. Archiv der Mathematik, 115(6), pp. 717-725. (doi: 10.1007/s00013-020-01517-5)

Cha, J. C., Kim, M. H. and Powell, M. (2020) A family of freely slice good boundary links. Mathematische Annalen, 376(3-4), pp. 1009-1030. (doi: 10.1007/s00208-019-01907-3)

Cha, J. C., Orr, K. E. and Powell, M. (2020) Whitney towers and abelian invariants of knots. Mathematische Zeitschrift, 294(1-2), pp. 519-553. (doi: 10.1007/s00209-019-02293-x)

Davis, C. W., Nagel, M., Orson, P. and Powell, M. (2020) Surface systems and triple linking numbers. Indiana University Mathematics Journal, 69(7), pp. 2505-2547. (doi: 10.1512/iumj.2020.69.8081)

Nagel, M., Orson, P., Park, J. and Powell, M. (2019) Smooth and topological almost concordance. International Mathematics Research Notices, 2019(23), pp. 7324-7355. (doi: 10.1093/imrn/rnx338)

Friedl, S., Nagel, M., Orson, P. and Powell, M. (2019) Satellites and concordance of knots in 3–manifolds. Transactions of the American Mathematical Society, 371(4), pp. 2279-2306. (doi: 10.1090/tran/7313)

Miller, A. N. and Powell, M. (2019) Stabilization distance between surfaces. L’Enseignement Mathématique, 65(3/4), pp. 397-440. (doi: 10.4171/lem/65-3/4-4)

Miller, A. N. and Powell, M. (2018) Symmetric chain complexes, twisted Blanchfield pairings and knot concordance. Algebraic and Geometric Topology, 18(6), pp. 3425-2476. (doi: 10.2140/agt.2018.18.3425)

Nagel, M. and Powell, M. (2017) Concordance invariance of Levine-Tristram signatures of links. Documenta Mathematica, 22, pp. 25-43. (doi: 10.25537/dm.2017v22.25-43)

Kasprowski, D., Land, M., Powell, M. and Teichner, P. (2017) Stable classification of 4-manifolds with 3-manifold fundamental groups. Journal of Topology, 10(3), pp. 827-881. (doi: 10.1112/topo.12025)

Powell, M. , Cochran, T. D. and Harvey, S. (2017) Grope metrics on the knot concordance set. Journal of Topology, 10(3), pp. 669-699. (doi: 10.1112/topo.12018)

Cha, J. C., Friedl, S. and Powell, M. (2017) Splitting numbers of links. Proceedings of the Edinburgh Mathematical Society, 60(3), pp. 587-614. (doi: 10.1017/S0013091516000420)

Powell, M. (2017) The four-genus of a link, Levine–Tristram signatures and satellites. Journal of Knot Theory and Its Ramifications, 26(2), 1740008. (doi: 10.1142/s0218216517400089)

Friedl, S. and Powell, M. (2017) A calculation of Blanchfield pairings of 3-manifolds and knots. Moscow Mathematical Journal, 17(1), pp. 59-77. (doi: 10.17323/1609-4514-2017-17-1-59-77)

Fruedk, S., Leidy, C., Nagel, M. and Powell, M. (2017) Twisted Blanchfield pairings and decompositions of 3-manifolds. Homology, Homotopy and Applications, 19(2), pp. 275-287. (doi: 10.4310/HHA.2017.v19.n2.a14)

Powell, M. (2016) Twisted Blanchfield pairings and symmetric chain complexes. Quarterly Journal of Mathematics, 67(4), pp. 715-742. (doi: 10.1093/qmath/haw028)

Cha, J. C. and Powell, M. (2016) Casson towers and slice links. Inventiones Mathematicae, 205(2), pp. 413-457. (doi: 10.1007/s00222-015-0639-z)

Borodzik, M., Friedl, S. and Powell, M. (2016) Blanchfield forms and Gordian distance. Journal of the Mathematical Society of Japan, 68(3), pp. 1047-1080. (doi: 10.2969/jmsj/06831047)

Borodzik, M. and Powell, M. (2016) Embedded Morse theory and relative splitting of cobordisms of manifolds. Journal of Geometric Analysis, 26(1), pp. 57-87. (doi: 10.1007/s12220-014-9538-6)

Friedl, S., Nagel, M. and Powell, M. (2014) A specious unlinking strategy. Periodica Mathematica Hungarica, 69(2), pp. 207-210. (doi: 10.1007/s10998-014-0063-y)

Cha, J. C., Friedl, S. and Powell, M. (2014) Concordance of links with identical Alexander invariants. Bulletin of the London Mathematical Society, 46(3), pp. 629-642. (doi: 10.1112/blms/bdu002)

Friedl, S. and Powell, M. (2014) Links not concordant to the Hopf link. Mathematical Proceedings of the Cambridge Philosophical Society, 156(3), pp. 425-459. (doi: 10.1017/S0305004114000036)

Friedl, S. and Powell, M. (2014) Cobordisms to weakly splittable links. Proceedings of the American Mathematical Society, 142(2), pp. 703-712. (doi: 10.1090/S0002-9939-2013-11792-2)

Cha, J. C. and Powell, M. (2014) Covering link calculus and the bipolar filtration of topologically slice links. Geometry and Topology, 18(3), pp. 1539-1579. (doi: 10.2140/gt.2014.18.1539)

Cha, J. C. and Powell, M. (2014) Nonconcordant links with homology cobordant zero-framed surgery manifolds. Pacific Journal of Mathematics, 272(1), pp. 1-33. (doi: 10.2140/PJM.2014.272.1)

Kasprowski, D. and Powell, M. (2014) Shrinking of toroidal decomposition spaces. Fundamenta Mathematicae, 227, pp. 271-296. (doi: 10.4064/fm227-3-3)

Friedl, S. and Powell, M. (2012) An injectivity theorem for Casson-Gordon type representations relating to the concordance of knots and links. Bulletin of the Korean Mathematical Society, 49(2), pp. 395-409. (doi: 10.4134/BKMS.2012.49.2.395)

Balm, C., Friedl, S., Kalfagianni, E. and Powell, M. (2012) Cosmetic crossings and Seifert matrices. Communications in Analysis and Geometry, 20(2), pp. 235-253. (doi: 10.4310/CAG.2012.v20.n2.a1)

Powell, M. (2012) A second order algebraic knot concordance group. Algebraic and Geometric Topology, 12(2), pp. 685-751. (doi: 10.2140/agt.2012.12.685)

Edited Books

Behrens, S., Kalmar, B., Kim, M. H., Powell, M. and Ray, A. (Eds.) (2021) The Disc Embedding Theorem. Oxford University Press: Oxford. ISBN 9780198841319

This list was generated on Sun Jul 21 22:07:16 2024 BST.

Grants

EPSRC New Investigator grant, Classifying 4-manifolds, 2021 - 2024.

EPSRC New Horizons grant, Symmetries of 4-manifolds, 2021 - 2023.

Supervision

  • Galvin, Daniel
    Non-smoothable homeomorphisms of 4-manifolds
  • Niu, Weizhe
    Mapping class groups of 4-manifolds via barbell diffeomorphisms, Budney-Gabai invariants and handle structures