Artin groups associated to infinite Coxeter groups

AbstractFirst we remark that the cellular complex constructed by Salvetti (1994) can be considered as a ‘topological’ invariant of a graph, so its cohomology is also an invariant. We use the construction of Salvetti (1994) to calculate the cohomology of the Artin group associated to the complete graph Kn, using coefficients in a local system over Z[q,q−1]. The standard cohomology over Z is obtained by specializing q to 1. While doing such computations, we obtain also an explicit rational function for the Poincaré series of the Coxeter group associated to Kπ, and note that it has exponential growth for n⩾4