On $h$-cobordisms of complexity $2$

Roberto Ladu

On $h$-cobordisms of complexity $2$

Geometric Topology 2025-06-23 v2

Authors: Roberto Ladu

Abstract

We study $5$ -dimensional $h$ -cobordisms of Morgan-Szab\'o complexity $2$ . We compute the monopole Floer homology and the action of the twisting involution of the protocork boundary associated with such $h$ -cobordisms, obtaining an obstruction for $h$ -cobordisms between exotic pairs to have minimal complexity. We construct the first examples of $h$ -cobordisms of non-minimal, in fact, arbitrarily large, complexity between an exotic pair of closed, $1$ -connected $4$ -manifolds. Further applications include strong corks.

Keywords

h-cobordism complexity monopole Floer homology exotic 4-manifolds Morgan-Szabó cork twisting involution action

Cite

@article{arxiv.2501.08750,
  title  = {On $h$-cobordisms of complexity $2$},
  author = {Roberto Ladu},
  journal= {arXiv preprint arXiv:2501.08750},
  year   = {2025}
}

Comments

23 pages, 14 figures. In this version we work over Z/2 instead of Z thus removing the dependence on the HF knot surgery exact sequence over Z while keeping our original applications

On $h$-cobordisms of complexity $2$

Abstract

Keywords

Cite

Comments

Related papers