Year: 2025
Type: preprint
Abstract: In all dimensions $n \ge 4$ not of the form $4m+3$, we show that there exists a closed hyperbolic $n$-manifold which is not the boundary of a compact $(n+1)$-manifold. The proof relies on the relationship between the cobordism class and the fixed point set of an involution on the manifold, together with a geodesic embedding of Kolpakov, Reid and Slavich. We also outline a possible approach to cover the dimensions $4m+3 \ne 2^k-1$.
Source: arXiv (Cornell University)
Author: Chen, Jacopo G.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4406736244