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arXiv · 2303.15981

On the \v{C}ech cohomology of Morse boundaries

Elia Fioravanti·Annette Karrer·Alessandro Sisto·Stefanie Zbinden
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Abstract

We consider cusped hyperbolic $n-$manifolds, and compute \v{C}ech cohomology groups of the Morse boundaries of their fundamental groups. In particular, we show that the reduced \v{C}ech cohomology with real coefficients vanishes in dimension at most $n-3$ and does not vanish in dimension $n-2$. A similar result holds for relatively hyperbolic groups with virtually nilpotent peripherals and Bowditch boundary homeomorphic to a sphere; these include all non-uniform lattices in rank$-1$ simple Lie groups.

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Elia Fioravanti, Annette Karrer, Alessandro Sisto, Stefanie Zbinden. 2023-03-28. On the \v{C}ech cohomology of Morse boundaries. https://doi.org/10.1016/j.aim.2024.109601

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