English

Infinite order corks

Geometric Topology 2017-06-14 v3

Abstract

We construct a compact, contractible 4-manifold CC, an infinite-order self-diffeomorphism ff of its boundary, and a smooth embedding of CC into a closed, simply connected 4-manifold XX, such that the manifolds obtained by cutting CC out of XX and regluing it by powers of ff are all pairwise nondiffeomorphic. The manifold CC can be chosen from among infinitely many homeomorphism types, all obtained by attaching a 2-handle to the meridian of a thickened knot complement.

Keywords

Cite

@article{arxiv.1603.05090,
  title  = {Infinite order corks},
  author = {Robert E. Gompf},
  journal= {arXiv preprint arXiv:1603.05090},
  year   = {2017}
}

Comments

6 pages, 2 figures. To appear in Geometry and Topology (v3). Discussion of Question 1.6 (meridian twists and more general knots) updated. Other minor improvements