Abstract We show that the relative cohomological dimension cdR (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 F ∞. As a corollary of our methods, we compute cd ₙ (G, H) cd Z (G, H) in several cases.
Harsh Patil (2026) studied this question.
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