On the Čech 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 Čech cohomology groups of the Morse boundaries of their fundamental groups. In particular, we show that the reduced Čech 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.
Original languageEnglish
Article number109601
JournalAdvances in Mathematics
Volume443
Early online date7 Mar 2024
DOIs
Publication statusPublished - May 2024

Keywords

  • Cech cohomology
  • Cusped hyperbolic manifold
  • Discrete homology
  • Morse boundary
  • Relatively hyperbolic
  • Sphere boundary

ASJC Scopus subject areas

  • General Mathematics

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