Amenable groups and smooth topology of 4-manifolds

Michael Freedman; Larry Guth; Emmy Murphy

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arXiv · 1503.05497

Amenable groups and smooth topology of 4-manifolds

Michael Freedman·Larry Guth·Emmy Murphy

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Abstract

A smooth five-dimensional s-cobordism becomes a smooth product if stabilized by a finite number n of $S^2xS^2x[0,1]$'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.

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Michael Freedman, Larry Guth, Emmy Murphy. 2015-03-18. Amenable groups and smooth topology of 4-manifolds. https://arxiv.org/abs/1503.05497

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