Relative bounded cohomology on groups with contracting elements
Abstract
Let G be a countable group acting properly on a metric space with contracting elements and fH i W 1 Ä i Ä ng be a finite collection of Morse subgroups in G.We prove that each H i has infinite index in G if and only if the relative second bounded cohomology H 2 b .G; fH i g n iD1 I R/ is infinite-dimensional.In addition, we also prove that for any contracting element g, there exists k > 0 such thatOur results generalize a theorem of Pagliantini-Rolli for finite-rank free groups and yield new results on the (relative) second bounded cohomology of groups.
Fields of Study & Subjects
Geometric and Algebraic Topology
Mathematical Dynamics and Fractals
Topological and Geometric Data Analysis
Publication details
- Journal / source
- Algebraic & Geometric Topology
- Volume
- 26
- Issue
- 3
- Pages
- 1195–1227
- Publication date
- 1 April 2026
- Language
- EN