Non-cobordant hyperbolic manifolds

2025/01/20 by Jacopo G. Chen, Chen, Jacopo G. · 1 citation
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2501.11610

openalex publication_date 2025/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In all dimensions n ≥ 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 ≠ 2^k-1.

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