Amenable groups and smooth topology of 4-manifolds

2015/03/18 by Michael Freedman, Larry Guth, Freedman, Michael +3
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG) #math.GT #math.MG

paper · pdf · doi:10.48550/arxiv.1503.05497

arxiv created 2015/03/18 · arxiv updated 2015/03/19

Abstract

A smooth five-dimensional s-cobordism becomes a smooth product if stabilized by a finite number n of S²xS²x[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.

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