Characterization of Y_2-equivalence for homology cylinders

Gwenael Massuyeau; Jean-Baptiste Meilhan

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Characterization of Y_2-equivalence for homology cylinders

Gwenael Massuyeau·Jean-Baptiste Meilhan

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Abstract

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.

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BibTeX RIS

Gwenael Massuyeau, Jean-Baptiste Meilhan. 2003-01-06. Characterization of Y_2-equivalence for homology cylinders. https://arxiv.org/abs/math/0203179

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