#### Volume 17, issue 5 (2017)

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Infinite order corks via handle diagrams

### Robert E Gompf

Algebraic & Geometric Topology 17 (2017) 2863–2891
##### 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 “$\delta$–moves” recently introduced by Akbulut are essentially equivalent to torus twists.

##### Keywords
cork, h-cobordism, 4-manifold
##### Mathematical Subject Classification 2010
Primary: 57N13, 57R55
##### 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