Topological boundaries of connected graphs and Coxeter groups

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Topological boundaries of connected graphs and Coxeter groups

Journal Article (2023)

Author(s)

Mario Klisse (TU Delft - Electrical Engineering, Mathematics and Computer Science)

Research Group

Analysis

Graphs Coxeter groups Iwahori–Hecke algebras Topological boundaries Topological compactifications

DOI related publication

https://doi.org/10.7900/jot.2021aug20.2348 Final published version

To reference this document use

https://resolver.tudelft.nl/uuid:7c32da77-06e4-4a68-b733-ae9e84d54845

More Info

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Publication Year

2023

Language

English

Research Group

Analysis

Issue number

2

Volume number

89

Pages (from-to)

429-476

Downloads counter

150

Abstract

We introduce and study certain topological spaces associated with connected rooted graphs. These spaces reflect combinatorial and order theoretic properties of the underlying graph and relate in the case of hyperbolic graphs to Gromov’s hyperbolic compactification. They are particularly tractable in the case of Cayley graphs of finite rank Coxeter systems and are intimately related to the corresponding Iwahori–Hecke algebras. We study this connection by considering dynamical properties of the induced action of the Coxeter group.