G-Corks and Heegaard Floer homology

Abstract

In [D. Auckly, H. J. Kim, P. Melvin and D. Ruberman, Equivariant corks, Algebr. Geom. Topol. 17(3) (2017) 1771–1783], Auckly–Kim–Melvin–Ruberman showed that for any finite subgroup [Formula: see text] of [Formula: see text] there exists a contractible smooth 4-manifold with an effective [Formula: see text]-action on its boundary so that the twists associated to the non-trivial elements of [Formula: see text] don’t extend to diffeomorphisms of the entire manifold. We give a different proof of this phenomenon using the Heegaard Floer techniques in [S. Akbulut and Ç. Karakurt, Action of the cork twist on Floer homology, in Proc. Gökova Geometry-Topology Conf. 2011 (International Press, Somerville, MA, 2012), pp. 42–52].