Computing the Cech cohomology of decomposition spaces

Benjamin Barrett

Computing the Cech cohomology of decomposition spaces

Benjamin Barrett

School of Mathematics

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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 language	English
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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1712.00780v1Submitted manuscript, 146 KBLicence: Unspecified

https://arxiv.org/abs/1712.00780

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title = "Computing the Cech cohomology of decomposition spaces",

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. ",

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publisher = "Cornell University",

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AB - 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.

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KW - math.GR

KW - 20E08, 20F10, 20F65, 57M07

M3 - Article (Academic Journal)

JO - arXiv

JF - arXiv

ER -

Computing the Cech cohomology of decomposition spaces

Abstract

Bibliographical note

Keywords

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