Computing the Cech cohomology of decomposition spaces

2017/12/03 by Benjamin Barrett, Barrett, Benjamin
Mathematics · #20E08 #20F10 #20F65 #57M07 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #math.GT #msc:20E08 #msc:20F10 #msc:20F65 #msc:57M07

paper · pdf · doi:10.48550/arxiv.1712.00780

10 pages, 2 figures

arxiv created 2017/12/03 · openalex publication_date 2017/12/03 · arxiv updated 2017/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A line pattern in a free group F is defined by a malnormal collection of cyclic subgroups. Otal defined a decomposition space D associated to a line pattern. We provide an algorithm that computes a presentation for the Čech cohomology of 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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