TOPOLOGICAL BOUNDARIES OF CONNECTED GRAPHS AND COXETER GROUPS

We introduce and study certain topological spaces associated with connected rooted graphs. These spaces reflect combinatorial and order theo-retic properties of the underlying graph and relate in the case of hyperbolic graphs to Gromov's hyperbolic compactification. They are particularly tracta-ble in the case of Cayley graphs of finite rank Coxeter systems and are inti-mately related to the corresponding Iwahori-Hecke algebras. We study this connection by considering dynamical properties of the induced action of the Coxeter group.