Homology cylinders: an enlargement of the mapping class group

Levine, Jerome¹

¹Department of Mathematics, Brandeis University, Waltham MA 02454-9110, USA

Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 243-270

Résumé

We consider a homological enlargement of the mapping class group, defined by homology cylinders over a closed oriented surface (up to homology cobordism). These are important model objects in the recent Goussarov–Habiro theory of finite-type invariants of 3–manifolds. We study the structure of this group from several directions: the relative weight filtration of Dennis Johnson, the finite-type filtration of Goussarov–Habiro, and the relation to string link concordance.

We also consider a new Lagrangian filtration of both the mapping class group and the group of homology cylinders.

Détail

DOI : 10.2140/agt.2001.1.243

Keywords: homology cylinder, mapping class group, clasper, finite-type invariant

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