Toric complexes and Artin kernels
| dc.creator | Papadima, Stefan | |
| dc.creator | Suciu, Alexander I. | |
| dc.date | 2008-01-23 | |
| dc.date | 2008-12-21 | |
| dc.date.accessioned | 2026-07-07T12:20:39Z | |
| dc.date.available | 2026-07-07T12:20:39Z | |
| dc.description | 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 χ\colon G_L\to \Z, let T_L^χbe the corresponding cover, with fundamental group the Artin kernel N_χ. We compute the cohomology jumping loci of the toric complex T_L, as well as the homology groups of T_L^χwith coefficients in a field \k, viewed as modules over the group algebra \k\Z. We give combinatorial conditions for H_{\le r}(T_L^χ;\k) to have trivial \Z-action, allowing us to compute the truncated cohomology ring, H^{\le r}(T_L^χ;\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. | |
| dc.description | 34 pages | |
| dc.identifier | https://arxiv.org/abs/0801.3626 | |
| dc.identifier | http://arxiv.org/abs/0801.3626 | |
| dc.identifier | Advances in Mathematics 220 (2009), no. 2, 441-477 | |
| dc.identifier | doi:10.1016/j.aim.2008.09.008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/213123 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Group Theory | |
| dc.subject | 20F36, 57M07 (Primary); 55N25, 55P62 (Secondary) | |
| dc.title | Toric complexes and Artin kernels | |
| dc.type | text |