Infinite reduced words and the Tits boundary of a Coxeter group
Thomas Lam and Anne Thomas
Abstract
Let be a finite rank Coxeter system with
infinite. We prove that the limit weak order on the blocks of
infinite reduced words of is encoded by the topology of
the Tits boundary of the Davis complex of
. We consider many special cases, including word
hyperbolic, and with isolated flats. We establish that
when is word hyperbolic, the limit weak order is the
disjoint union of weak orders of finite Coxeter groups. We
also establish, for each boundary point , a natural
order-preserving correspondence between infinite reduced words
which "point towards" , and elements of the reflection
subgroup of which fixes .
AMS Subject Classification:
Primary 20F55; secondary (primary), 52C35, 20F65 (secondary).