Computing the Cech cohomology of decomposition spaces

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Abstract

A line pattern in a free group $F$ is defined by a malnormal collection of cyclic subgroups. Otal defined a decomposition space $\mathcal{D}$ associated to a line pattern. We provide an algorithm that computes a presentation for the \v{C}ech cohomology of $\mathcal{D}$, thought of as a $F$-module. This answers a relative version of a question of Epstein about boundaries of hyperbolic groups.
Original languageEnglish
JournalarXiv
Publication statusSubmitted - 3 Dec 2017

Bibliographical note

10 pages, 2 figures

Keywords

  • math.GT
  • math.GR
  • 20E08, 20F10, 20F65, 57M07

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