## University of Sydney Algebra Seminar

# Anne Thomas (University of Sydney)

## Friday 14th June, 12:05-12:55pm, Carslaw 173

### Infinite reduced words and the Tits boundary of Coxeter groups

Let \((W,S)\) be a Coxeter system with W infinite. An infinite reduced word of \(W\) is an infinite sequence of elements of \(S\) such that each finite subsequence is a reduced word. We recall a natural partial order on infinite reduced words, called the limit weak order, which was investigated for \(W\) affine by Lam-Pylyavskyy. In order to study this partial order for W non-affine, we use the Davis complex \(X\) for \((W,S)\). Our main result says that the limit weak order is encoded by the topology of the Tits boundary of \(X\). No background on Davis complexes or the Tits boundary will be assumed. This is joint work with Thomas Lam.