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.
All Science Journal Classification (ASJC) codes
- Geometry and Topology
- amenable group