An invariant of corks

Roberto Ladu (Max Planck Institute for Mathematics)

Tuesday 9th May, 2023 11:00-12:00 Maths 311B

Abstract

Corks are a class of contractible 4-manifolds equipped with an involution of their boundary that can be used to produce exotic copies of closed 4-manifolds. Indeed is well known that any simply connected exotic pair is related by such operation. It is difficult to obtain general results about corks because we lack a classification of them. In order to solve this problem I will introduce a class of 4-manifolds, called protocorks, which are easily classified. The idea is that to study a cork we can study a supporting protocork. By doing so we can cook up an invariant defined as the U-torsion order of a special element in the cork's boundary Floer homology with Z/2Z coefficients. I will explain this and give some examples of applications.

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