### 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 |
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Journal | arXiv |

Publication status | Submitted - 3 Dec 2017 |

### Bibliographical note

10 pages, 2 figures### Keywords

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

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## Cite this

Barrett, B. (2017). Computing the Cech cohomology of decomposition spaces. Manuscript submitted for publication. https://arxiv.org/abs/1712.00780