Tangential thickness of manifolds

Abstract

Abstract. A notion of tangential thickness of a manifold is introduced. An extensive calculation within the class of lens and fake lens spaces leads to a classification of such manifolds with thickness 1, 3 or 2k, for k ≥ 1. On the other hand, calculations of tangential thickness in terms of the dimension of the manifold and the rank of the fundamental group show very interesting and quite surprising correlations between these invariants.

A simplification problem in manifold theory

“…Note that a diffeomorphism f : M × R k → N × R k induces a stable tangential homotopy equivalence (still called f ) from M to N . The thickness of such a stable tangential homotopy equivalence f is the minimal k for which f is induced by an R k -diffeomorphism [42]. This thickness is ≤ dim M + 2 [48,Theorem 1].…”