Calculating the homology of Coxeter groups
Rachael Boyd (Aberdeen)
Monday 14th November, 2016 16:00-17:00 Maths 204
Coxeter groups were introduced in the 1930s as abstractions of reflection groups: they are groups generated by involutions which satisfy some additional properties. They appear in areas of mathematics such as root systems and Lie theory, combinatorics, and geometric group theory. Any Coxeter group can be realised as a group generated by reflections on a contractible complex, called the Davis complex. By studying the stabilisers of cells of the Davis complex we are able to compute the first, second and third homology groups of an arbitrary Coxeter group using a spectral sequence argument. I will give a gentle introduction to Coxeter groups and the Davis complex before outlining the proof.