# 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.