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Equivariant corks and Heegaard Floer homology

Banff International Research Station for Mathematical Innovation and Discovery

A cork is a contractible smooth 4-manifold with an involution on its boundary that does not extend to a diffeomorphism of the entire manifold. Corks can be used to detect exotic structures; in fact, any two smooth structures on a closed simply-connected 4-manifold are related by a cork twist. Recently, Auckly-Kim-Melvin-Ruberman showed that for any finite subgroup G of SO(4) there exists a contractible 4-manifold with an effective G-action on its boundary so that the twists associated to the non-trivial elements of G do not extend to diffeomorphisms of the entire manifold. In this talk, we will use Heegaard Floer techniques originating in work of Akbulut-Karakurt to give a different proof of this phenomenon.

Mathematics; Manifolds and cell complexes; Global analysis, analysis on manifolds; Low dimensional topology

video/mp4

Author affiliation: Brandeis University

2018-02-04

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/64552

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/