PreprintCC BY 4.0arXiv
Integral cohomology of classical Artin groups: spherical types A,C,D and affine types B̃,C̃,D̃
Abstract
We determine the additive structure of the integral cohomology groups with trivial coefficients of the Artin groups in the spherical families An,Cn,Dn and the affine families B̃n,C̃n,D̃n. 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 p2 for any prime p. We also give uniform generating series formulas describing the stable integral cohomology in terms of that of the braid groups.
Related
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BibTeX
@misc{weinstein2026integral,
title = {{Integral cohomology of classical Artin groups: spherical types $A,C,D$ and affine types $\widetilde B,\widetilde C,\widetilde D$}},
author = {F. V. Weinstein},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.15419},
eprint = {2609.15419},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15419},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Integral cohomology of classical Artin groups: spherical types A,C,D and affine types B̃,C̃,D̃
AU - F. V. Weinstein
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2609.15419
UR - https://arxiv.org/abs/2609.15419
AB - 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 B̃_n,C̃_n,D̃_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.
ER -