Finite-type invariants of three-manifolds and the dimension subgroup problem
| dc.creator | Massuyeau, Gwenael | |
| dc.date | 2006-05-18 | |
| dc.date | 2006-12-13 | |
| dc.date.accessioned | 2026-07-07T08:46:14Z | |
| dc.date.available | 2026-07-07T08:46:14Z | |
| dc.description | For a certain class of compact oriented 3-manifolds, M. Goussarov and K. Habiro have conjectured that the information carried by finite-type invariants should be characterized in terms of ``cut-and-paste'' operations defined by the lower central series of the Torelli group of a surface. In this paper, we observe that this is a variation of a classical problem in group theory, namely the ``dimension subgroup problem.'' This viewpoint allows us to prove, by purely algebraic methods, an analogue of the Goussarov-Habiro conjecture for finite-type invariants with values in a fixed field. We deduce that their original conjecture is true at least in a weaker form. | |
| dc.description | 20 pages, 7 figures. Minor changes in this final version | |
| dc.identifier | https://arxiv.org/abs/math/0605497 | |
| dc.identifier | http://arxiv.org/abs/math/0605497 | |
| dc.identifier | J. London Math. Soc. 75:3 (2007) 791-811 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143186 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M27, 16S34 | |
| dc.title | Finite-type invariants of three-manifolds and the dimension subgroup problem | |
| dc.type | text |