Corks, exotic 4-manifolds and knot concordance

Kouichi Yasui

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arXiv · 1505.02551

Corks, exotic 4-manifolds and knot concordance

Kouichi Yasui

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Abstract

We show that, for each integer n, there exist infinitely many pairs of n-framed knots representing homeomorphic but non-diffeomorphic (Stein) 4-manifolds, which are the simplest possible exotic 4-manifolds regarding handlebody structures. To produce these examples, we introduce a new description of cork twists and utilize satellite maps. As an application, we produce knots with the same 0-surgery which are not concordant for any orientations, disproving the Akbulut-Kirby conjecture given in 1978.

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Kouichi Yasui. 2017-09-28. Corks, exotic 4-manifolds and knot concordance. https://arxiv.org/abs/1505.02551

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