Algebraic & Geometric Topology

Infinite order corks via handle diagrams

Robert Gompf

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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 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.

Article information

Algebr. Geom. Topol., Volume 17, Number 5 (2017), 2863-2891.

Received: 7 September 2016
Revised: 11 March 2017
Accepted: 22 March 2017
First available in Project Euclid: 16 November 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57N13: Topology of $E^4$ , $4$-manifolds [See also 14Jxx, 32Jxx] 57R55: Differentiable structures

cork h-cobordism 4-manifold


Gompf, Robert. Infinite order corks via handle diagrams. Algebr. Geom. Topol. 17 (2017), no. 5, 2863--2891. doi:10.2140/agt.2017.17.2863.

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