Infinite order corks via handle diagrams

Gompf, Robert

doi:10.2140/agt.2017.17.2863

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Infinite order corks via handle diagrams

Robert E Gompf

Algebraic & Geometric Topology 17 (2017) 2863–2891

DOI: 10.2140/agt.2017.17.2863

Abstract

The author recently proved the existence of an infinite order cork: a compact, contractible submanifold $C$ of a 4–manifold and an infinite order diffeomorphism $f$ of $\partial C$ such that cutting out $C$ and regluing it by distinct powers of $f$ yields pairwise nondiffeomorphic manifolds. The present paper exhibits the first handle diagrams of this phenomenon, by translating the earlier proof into this language (for each of the infinitely many corks arising in the first paper). The cork twists in these papers are twists on incompressible tori. We give conditions guaranteeing that such twists do not change the diffeomorphism type of a 4–manifold, partially answering a question from the original paper. We also show that the “ $δ$ –moves” recently introduced by Akbulut are essentially equivalent to torus twists.

Keywords

cork, h-cobordism, 4-manifold

Mathematical Subject Classification 2010

Primary: 57N13, 57R55

References

Publication

Received: 7 September 2016

Revised: 11 March 2017

Accepted: 22 March 2017

Published: 19 September 2017

Authors

Robert E Gompf
Department of Mathematics The University of Texas Austin, TX United States

Volume 17, issue 5 (2017)