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 '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.
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}
}