Relative cohomological dimension of a relatively hyperbolic pair

2025/05/07 by Harsh Patil, Patil, Harsh
Mathematics · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Geometry and complex manifolds

paper · doi:10.48550/arxiv.2505.04349

Abstract

We show that the relative cohomological dimension \cd(G,H) of a relatively hyperbolic pair (G,H) is always finite when G is torsion-free. We also show that this dimension is preserved under quasi-isometries, provided that G is torsion-free and the peripheral subgroup H is unconstricted and of type F_∞. As a corollary of our methods, we compute \cd(G,H) in a range of cases.

Citations

• Finiteness properties and Relatively Hyperbolic Groups
• Cohomology of group theoretic Dehn fillings II
• Relatively hyperbolic groups with fixed peripherals
• Quasi-Isometries, Boundaries and JSJ-Decompositions of Relatively Hyperbolic Groups
• Peripheral fillings of relatively hyperbolic groups
• Tree-graded spaces and asymptotic cones of groups
• Tree-graded spaces and asymptotic cones of groups
• The quasi-isometry classification of rank one lattices

Related

• A characterization of relatively hyperbolic groups via bounded cohomology
• Relatively hyperbolic groups: geometry and quasi-isometric invariance
• Relatively hyperbolic groups with fixed peripherals
• Subgroups of Relatively Hyperbolic Groups of Bredon Cohomological\n Dimension 2
• On Bestvina-Mess Formula