Homology cylinders: an enlargement of the mapping class group

Details Homology cylinders: an enlargement of the mapping class group Homology cylinders: an enlargement of the mapping class group

2000-10-26

arxiv.org/abs/math/0010247v2

Algebr. Geom. Topol. 1 (2001) 243-270

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-12.abs.html

Scientific paper

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.

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