Contracting boundaries of right-angled Coxeter and Artin groups

Annette Karrer (McGill)

04-Oct-2022, 13:00-15:00 (19 months ago)

Abstract: A complete CAT(0) space has a topological space associated to it called the contracting or Morse boundary. This boundary captures how similar the CAT(0) space is to a hyperbolic space. Charney--Sultan proved this boundary is a quasi-isometry invariant, i.e. it can be defined for CAT(0) groups. Interesting examples arise among contracting boundaries of right-anlged Artin and Coxeter groups.

The talk will consist of two parts. The first 45 minutes will be about the main result of my PhD project. We will study the question of how the contracting boundary of a right-connected Coxeter group changes when we glue certain graphs on its defining graph. We will focus on the question of when the resulting graph corresponds to a right-angled Coxeter group with totally disconnected contracting boundary.

After a short break, we will see a second result of my PhD thesis concerning the question of what happens if we glue a path of length at least two to a defining graph of a RACG. Afterwards, we will use our insights to investigate contracting boundaries of certain RACGs that contain surprising circles. These examples are joint work with Marius Graeber, Nir Lazarovich, and Emily Stark. Finally, we will transfer the ideas we saw before to RAAGs. This will result in a proof that all right-angled Artin groups have totally disconnected contracting boundaries, reproving a result of Charney--Cordes--Sisto.

algebraic topologyfunctional analysisgroup theorygeometric topologyoperator algebras

Audience: researchers in the topic


Vienna Geometry and Analysis on Groups Seminar

Organizer: Christopher Cashen*
*contact for this listing

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