Finite cuts and CAT(0) boundaries

2018/07/11 by Panos Papasoglu, Papasoglu, Panos, Eric Swenson +1
Mathematics · #20E08 #20F65 #54F05 #54F15 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.GR #msc:20E08 #msc:20F65 #msc:54F05 #msc:54F15

paper · pdf · doi:10.48550/arxiv.1807.04086

84 pages

arxiv created 2018/07/11 · openalex publication_date 2018/07/11 · arxiv updated 2018/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if a 1-ended group G acts geometrically on a CAT(0) space X and \bd X is separated by m points then either G is virtually a surface group or G splits over a 2-ended group. In the course of the proof we study nesting actions on \R -trees and we show that nesting actions with non overlapping translation intervals give rise to isometric actions.

Citations

• The structure of finitary permutation groups

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