Homology cylinders: an enlargement of the mapping class group

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.

Keywords

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

Mathematical Subject Classification 2000

Primary: 57N10

Secondary: 57M25

References

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Publication

Received: 14 November 2000

Accepted: 17 April 2001

Published: 23 April 2001

Authors

Jerome Levine
Department of Mathematics Brandeis University Waltham MA 02454-9110 USA
www.math.brandeis.edu/Faculty/jlevine/

Volume 1, issue 1 (2001)

Jerome Levine