Toric complexes and Artin kernels

• Autores: Stefan Papadima, Alexander I. Suciu
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 220, Nº 2, 2009, págs. 441-477
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.09.008
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• Resumen

  • A simplicial complex L on n vertices determines a subcomplex TL of the n-torus, with fundamental group the right-angled Artin group GL. Given an epimorphism , let be the corresponding cover, with fundamental group the Artin kernel N?. We compute the cohomology jumping loci of the toric complex TL, as well as the homology groups of with coefficients in a field , viewed as modules over the group algebra . We give combinatorial conditions for to have trivial -action, allowing us to compute the truncated cohomology ring, . We also determine several Lie algebras associated to Artin kernels, under certain triviality assumptions on the monodromy -action, and establish the 1-formality of these (not necessarily finitely presentable) groups.