Corks, exotic 4-manifolds and knot concordance
Geometric Topology
2017-09-29 v4 Symplectic Geometry
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.
Keywords
Cite
@article{arxiv.1505.02551,
title = {Corks, exotic 4-manifolds and knot concordance},
author = {Kouichi Yasui},
journal= {arXiv preprint arXiv:1505.02551},
year = {2017}
}
Comments
25 pages, 26 figures, Theorems 1.5 and 1.6 added, minor corrections