English

Amenable groups and smooth topology of 4-manifolds

Geometric Topology 2015-03-19 v1 Metric Geometry

Abstract

A smooth five-dimensional s-cobordism becomes a smooth product if stabilized by a finite number n of S2xS2x[0,1]S^2xS^2x[0,1]'s. We show that for amenable fundamental groups, the minimal n is subextensive in covers, i.e., n(cover)/index(cover) has limit 0. We focus on the notion of sweepout width, which is a bridge between 4-dimensional topology and coarse geometry.

Keywords

Cite

@article{arxiv.1503.05497,
  title  = {Amenable groups and smooth topology of 4-manifolds},
  author = {Michael Freedman and Larry Guth and Emmy Murphy},
  journal= {arXiv preprint arXiv:1503.05497},
  year   = {2015}
}