Hall invariants, homology of subgroups, and characteristic varieties
| dc.creator | Matei, Daniel | |
| dc.creator | Suciu, Alexander I. | |
| dc.date | 2000-10-04 | |
| dc.date.accessioned | 2026-07-07T04:37:51Z | |
| dc.date.available | 2026-07-07T04:37:51Z | |
| dc.description | Given a finitely-generated group G, and a finite group Γ, Philip Hall defined δ_Γto be the number of factor groups of G that are isomorphic to Γ. We show how to compute the Hall invariants by cohomological and combinatorial methods, when G is finitely-presented, and Γbelongs to a certain class of metabelian groups. Key to this approach is the stratification of the character variety by the jumping loci of the cohomology of G, with coefficients in rank 1 local systems over a suitably chosen field \K. Counting relevant torsion points on these "characteristic" subvarieties gives δ_Γ(G). In the process, we compute the distribution of prime-index, normal subgroups K of G according to the dimension of the the first homology group of K with \K coefficients, provided \char\K does not divide the index of K in G. In turn, we use this distribution to count low-index subgroups of G. We illustrate these techniques in the case when G is the fundamental group of the complement of an arrangement of either affine lines in \C^2, or transverse planes in \R^4. | |
| dc.description | 34 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0010046 | |
| dc.identifier | http://arxiv.org/abs/math/0010046 | |
| dc.identifier | International Math. Research Notices 2002:9 (2002), 465-503 | |
| dc.identifier | doi:10.1155/S107379280210907X | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60056 | |
| dc.subject | Group Theory | |
| dc.subject | Combinatorics | |
| dc.subject | Geometric Topology | |
| dc.subject | 20J05, 57M05 (primary), 20E07, 52C35 (secondary) | |
| dc.title | Hall invariants, homology of subgroups, and characteristic varieties | |
| dc.type | text |