Algebraic and Geometric Topology 1 (2001),
paper no. 12, pages 243-270.
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
We also consider a new Lagrangian filtration of both
the mapping class group and the group of homology cylinders.
Homology cylinder, mapping class group, clasper, finite-type invariant
AMS subject classification.
Submitted: 14 November 2000.
Accepted: 17 April 2001.
Published: 23 April 2001.
Notes on file formats
Department of Mathematics, Brandeis University
Waltham, MA 02454-9110, USA
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