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Contracting boundaries of right-angled Coxeter groups

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Annette Karrer (Technion)

Abstract: Associated to a complete CAT(0) space is a topological space called a contracting or Morse boundary. This boundary indicates how similar the CAT(0) space is to a hyperbolic space. Charney-Sultan proved that this boundary is a quasi-isometric invariant, i.e., it can be defined for CAT(0) groups.
In this talk we will study contracting boundaries of right-angled Coxeter groups. Right-angled Coxeter groups are CAT(0) groups defined by graphs. In the main part of the talk, we will study when the contracting boundary of a right-angled Coxeter group with totally disconnected contracting boundary remains totally disconnected if we glue certain graphs on its defining graph. This was part of my dissertation. At the end of the talk, we will use our insights to discuss an interesting example where surprising circles appear in the contracting boundary. This was joint work with Marius Graeber, Nir Lazarovich, and Emily Stark.