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Toric complexes and Artin kernels

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: S. Papadima, A. I. Suciu

Editorial: Advances in Mathematics, 220 (2), p. 441-477, 2009.

Rezumat:

A simplicial complex L on n vertices determines a subcomplex T_L of the n-torus, with fundamental group the right-angled Artin group G_L. Given an epimorphism chicolon G_Lto Z, let T_L^chi be the corresponding cover, with fundamental group the Artin kernel N_chi. We compute the cohomology jumping loci of the toric complex T_L, as well as the homology groups of T_L^chi with coefficients in a field k, viewed as modules over the group algebra kZ. We give combinatorial conditions for H_{le r}(T_L^chi;k) to have trivial Z-action, allowing us to compute the truncated cohomology ring, H^{le r}(T_L^chi;k). We also determine several Lie algebras associated to Artin kernels, under certain triviality assumptions on the monodromy Z-action, and establish the 1-formality of these (not necessarily finitely presentable) groups.

Cuvinte cheie: Toric complex, right-angled Artin group, Artin kernel, Bestvina–Brady group, cohomology ring, Stanley–Reisner ring, cohomology jumping loci, monodromy action, holonomy Lie algebra, Malcev Lie algebra, formality

URL: http://dx.doi.org/10.1016/j.aim.2008.09.008