# Computing the Cech cohomology of decomposition spaces

Research output: Contribution to journalArticle (Academic Journal)

### 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 language English arXiv Submitted - 3 Dec 2017

### Bibliographical note

10 pages, 2 figures

### Keywords

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