Integral cohomology of classical Artin groups: spherical types $A,C,D$ and affine types $\widetilde B,\widetilde C,\widetilde D$
Year: 2026
Type: preprint
Abstract: We determine the additive structure of the integral cohomology groups with trivial coefficients of the Artin groups in the spherical families $A_n,C_n,D_n$ and the affine families $\widetilde B_n,\widetilde C_n,\widetilde D_n$. We first compute the integral cohomology of braid groups by algebraic methods and then use the Salvetti complexes to express the cohomology of the remaining families in terms of these computations. The resulting descriptions apply in every admissible rank. For each family, we establish cohomological stabilization and show that the integral cohomology groups contain no elements of order $p^2$ for any prime $p$. We also give uniform generating series formulas describing the stable integral cohomology in terms of that of the braid groups.
Source: arXiv (Cornell University)
Author: Weinstein, F. V.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213230536