Mapping class groups of $h$-cobordant manifolds
Algebraic Topology
2026-02-10 v3 Geometric Topology
Abstract
We prove that the mapping class group is not an -cobordism invariant of high-dimensional manifolds by exhibiting -cobordant manifolds whose mapping class groups have different cardinalities. In order to do so, we introduce a moduli space of "-block" bundles and understand its difference with the moduli space of ordinary block bundles.
Keywords
Cite
@article{arxiv.2210.06573,
title = {Mapping class groups of $h$-cobordant manifolds},
author = {Samuel Muñoz-Echániz},
journal= {arXiv preprint arXiv:2210.06573},
year = {2026}
}
Comments
v2: 34 pages, 4 figures. Minor changes. Final version, similar to published version at Forum of Mathematics, Sigma