Bordisms and unbounded KK-theory

Magnus Goffeng (University of Lund)

Thursday 11th November, 2021 16:00-17:00 Maths 311B


Kasparov’s KK-theory has since its conceptions proven to be a highly useful tool in operator algebras and index theory. For geometric applications, the unbounded model of KK has proven to be interesting with Connes’ notion of noncommutative geometry through spectral triples appearing as a special case. This talk treats the notion of bordism in unbounded KK-theory, extended from manifolds to KK by Hilsum. We will in this talk see how bordism defines an equivalence relation on the unbounded KK-cycles and the equivalence classes form an abelian group. This abelian group is (under mild assumptions) isomorphic to the ordinary KK-group. Joint work with Robin Deeley and Bram Mesland.

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