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Some groups with planar boundaries

2019/07/16 by Sang-Hyun Kim, Kim, Sang-hyun, Genevieve Walsh +1
Mathematics · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1907.06898

Abstract

In this expository note, we illustrate phenomena and conjectures about boundaries of hyperbolic groups by considering the special cases of certain amalgams of hyperbolic groups. While doing so, we describe fundamental results on hyperbolic groups and their boundaries by Bowditch and Haissinsky, along with special treatments for the boundaries of free groups by Otal and Cashen.

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