University of Sydney Algebra Seminar

Anne Thomas (Cornell University)

Friday 3rd July, 12.05-12.55pm, Carslaw 375

Existence, covolumes and infinite generation of lattices for Davis complexes

Let $\Sigma$ be the Davis complex for a Coxeter system $(W,S)$. The automorphism group $G$ of $\Sigma$ is naturally a locally compact group, and a simple combinatorial condition due to Haglund--Paulin determines when $G$ is nondiscrete. The Coxeter group $W$ may be regarded as a uniform lattice in $G$. We show that many such $G$ also admit a uniform lattice $\Gamma$, and an infinite family of nonuniform lattices with covolumes converging to that of $\Gamma$. We also show that the nonuniform lattice $\Gamma$ is not finitely generated.