29 apr 2025 -- 14:30
aula Riunioni - Dipartimento di Matematica, Pisa
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 ≠ 2k−1.