Amenable groups and smooth topology of 4-manifolds

Michael Freedman; Larry Guth; Emmy Murphy

doi:10.1142/S1793525317500017

Amenable groups and smooth topology of 4-manifolds

Michael Freedman
, Larry Guth
, Emmy Murphy

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A smooth five-dimensional s-cobordism becomes a smooth product if stabilized by a finite number n of (S² × S² × [0, 1])'s. We show that for amenable fundamental groups, the minimal n is subextensive in covers, i.e. n(cover)/index cover→ 0. We focus on the notion of sweepout width, which is a bridge between 4-dimensional topology and coarse geometry.

Original language	English (US)
Pages (from-to)	1-14
Number of pages	14
Journal	Journal of Topology and Analysis
Volume	9
Issue number	1
DOIs	https://doi.org/10.1142/S1793525317500017
State	Published - Mar 1 2017

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

Keywords

amenable group
s-cobordism
stabilization
sweepout

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10.1142/S1793525317500017

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abstract = "A smooth five-dimensional s-cobordism becomes a smooth product if stabilized by a finite number n of (S2 × S2 × [0, 1])'s. We show that for amenable fundamental groups, the minimal n is subextensive in covers, i.e. n(cover)/index cover→ 0. We focus on the notion of sweepout width, which is a bridge between 4-dimensional topology and coarse geometry.",

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AU - Murphy, Emmy

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AB - A smooth five-dimensional s-cobordism becomes a smooth product if stabilized by a finite number n of (S2 × S2 × [0, 1])'s. We show that for amenable fundamental groups, the minimal n is subextensive in covers, i.e. n(cover)/index cover→ 0. We focus on the notion of sweepout width, which is a bridge between 4-dimensional topology and coarse geometry.

KW - amenable group

KW - s-cobordism

KW - stabilization

KW - sweepout

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UR - https://www.scopus.com/pages/publications/84964050251#tab=citedBy

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ER -

Amenable groups and smooth topology of 4-manifolds

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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