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 (7)

• A universal characterization of higher algebraic K-theory
• On the K-theory of pullbacks
• Generalised Miller-Morita-Mumford classes for block bundles and topological bundles
• A vanishing theorem for tautological classes of aspherical manifolds
• On characteristic classes of exotic manifold bundles
• How different can h-cobordant manifolds be?
• A Weiss-Williams theorem for spaces of embeddings and the homotopy type of spaces of long knots