The topological 4-genus of satellite knots.
Juanita Pinzón-Caicedo (University of Notre Dame - MPI)
Monday 23rd September, 2019 16:00-17:00 Maths 311B
A satellite knot P(K) is obtained by tying a given knot P inside a solid torus V along another knot K. The winding number w of the satellite operation is given by the algebraic intersection number of P with a meridional disk of the solid torus V. A result of Schubert states that for any pattern P with winding number w, there exists a constant g3(P) such that for any nontrivial knot K in S3 we have g3(P (K)) = g3(P ) + |w|g3(K). In joint work with Allison Miller and Peter Feller we show that in the smooth category an analogous formula holds, but in the topological category the winding number of the pattern is no longer pivotal.