Chapter 20 - Topological Rigidity Theorems

Abstract

Two topological manifolds which are properly homotopy equivalent may easily fail to be homeomorphic, Since the 1930s the lens spaces L (7, 1) and L (7, 2) have been known to behomotopy equivalent but not simple homotopy equivalent [ 29 ], for example, and the topological invariance of Whitehead torsion [ 24 ] shows that manifolds which are not simple homotopy equivalent are not homeomorphic.