G-corks & Heegaard Floer Homology

TL;DR

This paper provides a new proof, using Heegaard Floer homology, of a phenomenon where certain group actions on the boundary of a contractible 4-manifold do not extend to the whole manifold, originally shown by Auckly et al.

Contribution

It introduces a Heegaard Floer theoretic approach to demonstrate non-extendability of boundary group actions on contractible 4-manifolds, offering an alternative proof to prior results.

Findings

Heegaard Floer homology can detect non-extendable boundary actions.

Provides a new proof of a known phenomenon using Floer theoretic methods.

Shows the effectiveness of Floer homology in 4-manifold symmetry problems.

Abstract

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. We use a Heegaard Floer theoretic argument originating in work of Akbulut-Karakurt to give a different proof of this phenomenon.