Contributed Talk – The low dimensional homology of Coxeter groups – Rachael Boyd (Norwegian University of Science and Technology)

December 6, 2018 @ 3:00 pm – 3:30 pm
Seminar Room 1
Newton Institute

Coxeter groups were introduced by Tits in the 1960s as abstractions of the finite reflection groups studied by Coxeter. Any Coxeter group acts by reflections on a contractible complex, called the Davis complex. This talk focuses on a computation of the first three integral homology groups of an arbitrary Coxeter group using an isotropy spectral sequence argument: the answer can be phrased purely in terms of the original Coxeter diagram. I will give an introduction to Coxeter groups and the Davis complex before outlining the proof.