Homotopy equivalence and simple homotopy equivalence of manifoldsMPIM

by Csaba Nagy (MPIM)

Thursday Jan 29, 2026, 3:00 PM → 4:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

MPI-Oberseminar

A homotopy equivalence between finite CW-complexes is called simple if it is homotopic to a composition of elementary collapses and expansions. Lens spaces provide famous examples of manifolds that are homotopy equivalent but not simple homotopy equivalent to each other, in all ≥3≥3 odd dimensions. However, no even-dimensional examples are known in the literature.

We construct even-dimensional manifolds that are homotopy equivalent (in fact h-cobordant) but not simple homotopy equivalent to each other. More generally, we give a purely algebraic characterisation of groups G with the property that there exists a pair of manifolds with fundamental group G that are h-cobordant but not simple homotopy equivalent.

This is joint work with Johnny Nicholson and Mark Powell.