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Article Dans Une Revue J. Knot Th. Ramifications Année : 2003

Characterization of Y_2-equivalence for homology cylinders

Résumé

For S a compact connected oriented surface, we consider homology cylinders over S: these are homology cobordisms with an extra homological triviality condition. When considered up to Y_2-equivalence, which is a surgery equivalence relation arising from the Goussarov-Habiro theory, homology cylinders form an Abelian group. In this paper, when S has one or zero boundary component, we define a surgery map from a certain space of graphs to this group. This map is shown to be an isomorphism, with inverse given by some extensions of the first Johnson homomorphism and Birman-Craggs homomorphisms.

Dates et versions

hal-00135057 , version 1 (06-03-2007)

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Gwenael Massuyeau, Jean-Baptiste Meilhan. Characterization of Y_2-equivalence for homology cylinders. J. Knot Th. Ramifications, 2003, 12 (4), pp.493-522. ⟨hal-00135057⟩
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