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Article Dans Une Revue J. London Math. Society Année : 2007

Finite-type invariants of three-manifolds and the dimension subgroup problem

Résumé

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.

Dates et versions

hal-00135211 , version 1 (07-03-2007)

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Citer

Gwenael Massuyeau. Finite-type invariants of three-manifolds and the dimension subgroup problem. J. London Math. Society, 2007, 75 (3), pp.791-811. ⟨hal-00135211⟩
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