Amenable groups and smooth topology of 4-manifolds

Michael Freedman, Larry Guth, Emmy Murphy

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)1-14
Number of pages14
JournalJournal of Topology and Analysis
Issue number1
StatePublished - Mar 1 2017

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology


  • amenable group
  • s-cobordism
  • stabilization
  • sweepout


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