Jerome Levine
Published 2000-10-26, updated 2001-04-24Version 2
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.
Comments: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-12.abs.html
Journal: Algebr. Geom. Topol. 1 (2001) 243-270
Addendum and correction to: Homology cylinders: an enlargement of the mapping class group
Mapping class groups of once-stabilized Heegaard splittings
Some homological invariants of mapping class group of a 3-dimensional handlebody
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