Formality, Alexander invariants, and a question of Serre
| dc.creator | Dimca, Alexandru | |
| dc.creator | Papadima, Stefan | |
| dc.creator | Suciu, Alexander I. | |
| dc.date | 2005-12-21 | |
| dc.date | 2007-12-08 | |
| dc.date.accessioned | 2026-07-07T08:47:47Z | |
| dc.date.available | 2026-07-07T08:47:47Z | |
| dc.description | We elucidate the key role played by formality in the theory of characteristic and resonance varieties. We show that the I-adic completion of the Alexander invariant of a 1-formal group G is determined solely by the cup-product map in low degrees. It follows that the germs at the origin of the characteristic and resonance varieties of G are analytically isomorphic; in particular, the tangent cone to V_k(G) at 1 equals R_k(G). This provides new obstructions to 1-formality. A detailed analysis of the irreducible components of the tangent cone at 1 to the first characteristic variety yields powerful obstructions to realizing a finitely presented group as the fundamental group of a smooth, complex quasi-projective algebraic variety. This sheds new light on a classical problem of J.-P. Serre. Applications to arrangements, configuration spaces, coproducts of groups, and Artin groups are given. | |
| dc.description | 43 pages, updated references | |
| dc.identifier | https://arxiv.org/abs/math/0512480 | |
| dc.identifier | http://arxiv.org/abs/math/0512480 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143721 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14F35, 20F14, 55N25; 14M12, 20F36, 55P62 | |
| dc.title | Formality, Alexander invariants, and a question of Serre | |
| dc.type | text |