Homology cylinders: an enlargement of the mapping class group
Geometric Topology
2014-10-01 v2 Quantum Algebra
Abstract
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
Cite
@article{arxiv.math/0010247,
title = {Homology cylinders: an enlargement of the mapping class group},
author = {Jerome Levine},
journal= {arXiv preprint arXiv:math/0010247},
year = {2014}
}
Comments
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-12.abs.html