Higher-Order Polynomial Invariants of 3-Manifolds Giving Lower Bounds for the Thurston Norm
| dc.creator | Harvey, Shelly | |
| dc.date | 2002-07-01 | |
| dc.date.accessioned | 2026-07-07T06:31:43Z | |
| dc.date.available | 2026-07-07T06:31:43Z | |
| dc.description | We define an infinite sequence of new invariants, delta_n, of a group G that measure the size of the successive quotients of the derived series of G. In the case that G is the fundamental group of a 3-manifold, we obtain new 3-manifold invariants. These invariants are closely related to the topology of the 3-manifold. They give lower bounds for the Thurston norm which provide better estimates than the bound established by McMullen using the Alexander norm. We also show that the delta_n give obstructions to a 3-manifold fibering over S^1 and to a 3-manifold being Seifert fibered. Moreover, we show that the delta_n give computable algebraic obstructions to a 4-manifold of the form X x S^1 admitting a symplectic structure even when the obstructions given by the Seiberg-Witten invariants fail. There are also applications to the minimal ropelength and genera of knots and links in S^3. | |
| dc.identifier | https://arxiv.org/abs/math/0207014 | |
| dc.identifier | http://arxiv.org/abs/math/0207014 | |
| dc.identifier | Topology 44 (2005), no. 5, 895--945. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98687 | |
| dc.subject | Geometric Topology | |
| dc.subject | Group Theory | |
| dc.subject | 57M | |
| dc.title | Higher-Order Polynomial Invariants of 3-Manifolds Giving Lower Bounds for the Thurston Norm | |
| dc.type | text |