Cohomology Jumping Loci and Relative Malcev Completion
| dc.creator | Narkawicz, Anthony | |
| dc.date | 2008-04-25 | |
| dc.date.accessioned | 2026-07-07T09:35:20Z | |
| dc.date.available | 2026-07-07T09:35:20Z | |
| dc.description | Two standard invariants used to study the fundamental group G of the complement X of a hyperplane arrangement are the Malcev completion of G and the cohomology groups of X with coefficients in rank one local systems. In this paper, we develop a tool that unifies these two approaches. This tool is the Malcev completion S_p of G relative to a homomorphism p from G into (C^*)^N. This is a prosolvable group that is tightly controlled by the cohomology groups of X with coefficients in rank one local systems. The prounipotent radical U_p of the relative completion S_p corresponds to a pronilpotent Lie algebra u_p. We provide an example of a hyperplane complement X for which this algebra is not quadratically presented. In addition, we show that if X is a hyperplane complement and Y is a subtorus of the character torus, then S_p is combinatorially determined for general p in Y. Finally, we show that the relative completion S_p is generally constant over subvarieties of the character torus. | |
| dc.description | 54 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/0804.4164 | |
| dc.identifier | http://arxiv.org/abs/0804.4164 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159802 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Combinatorics | |
| dc.subject | 55N25; 16E45; 52C35; 55P62; 17D10 | |
| dc.title | Cohomology Jumping Loci and Relative Malcev Completion | |
| dc.type | text |