The parity of the Cochran-Harvey invariants of 3-manifolds
| dc.creator | Friedl, Stefan | |
| dc.creator | Kim, Taehee | |
| dc.date | 2005-10-21 | |
| dc.date | 2006-02-18 | |
| dc.date.accessioned | 2026-07-07T06:47:47Z | |
| dc.date.available | 2026-07-07T06:47:47Z | |
| dc.description | Given a finitely presented group G and an epimorphism G to the group of integers Cochran and Harvey defined a sequence of integral invariants, which can be viewed as the degrees of higher--order Alexander polynomials. Cochran and Harvey showed that (up to a minor modification) this is a never decreasing sequence of numbers if G is the fundamental group of a 3-manifold with empty or toroidal boundary, and that these invariants give lower bounds on the Thurston norm. Using a certain Cohn localization and the duality of Reidemeister torsion we show that for a fundamental group of a 3--manifold any jump in the sequence is necessarily even. This answers in particular a question of Cochran. Furthermore using results of Turaev we show that under a mild extra hypothesis the parity of the Cochran--Harvey invariant agrees with the parity of the Thurston norm. | |
| dc.description | 15 pages, accepted for publicaton by the Transactions of the AMS | |
| dc.identifier | https://arxiv.org/abs/math/0510475 | |
| dc.identifier | http://arxiv.org/abs/math/0510475 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103770 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25 (primary), 57M05 (secondary) | |
| dc.title | The parity of the Cochran-Harvey invariants of 3-manifolds | |
| dc.type | text |