Relative cohomological dimension of a relatively hyperbolic pair
Abstract
Abstract We show that the relative cohomological dimension $$\textrm{cd}_R(G,H)$$ cd R ( G , H ) of a relatively hyperbolic pair ( G , H ) is always finite when G does not contain R -torsion. 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 $$F_{\infty }$$ F ∞ . As a corollary of our methods, we compute $$\textrm{cd}_{\mathbb {Z}}(G,H)$$ cd Z ( G , H ) in several cases.
Fields of Study & Subjects
Geometric and Algebraic Topology
Mathematical Dynamics and Fractals
Geometry and complex manifolds
Publication details
- Journal / source
- Journal of Homotopy and Related Structures
- Volume
- 21
- Issue
- 3
- Pages
- 491–508
- Publication date
- 26 February 2026
- Language
- EN