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Corks, exotic 4-manifolds and knot concordance

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arxiv 1505.02551 v4 pith:Q3BKH7KT submitted 2015-05-11 math.GT math.SG

Kouichi Yasui This is my paper · ORCID
classification math.GTmath.SG
keywords manifoldsexoticknotsproduceakbulut-kirbyapplicationconcordanceconcordant
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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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  1. Strong corks derived from the Akbulut cork

    math.GT 2026-01 conditional novelty 6.0 of 10

    The boundaries of the AKMR and Tange cork families, and nontrivial equivariant connected sums of them, are strong corks.

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