Mapping class groups of $h$-cobordant manifolds

Abstract

We prove that the mapping class group is not an $h$-cobordism invariant of high-dimensional manifolds by exhibiting $h$-cobordant manifolds whose mapping class groups have different cardinalities. In order to do so, we introduce a moduli space of "$h$-block" bundles and understand its difference with the moduli space of ordinary block bundles.

v2: 34 pages, 4 figures. Minor changes. Final version, similar to published version at Forum of Mathematics, Sigma

References in corpus (1)

• A Weiss-Williams theorem for spaces of embeddings and the homotopy type of spaces of long knots