Algebraic & Geometric Topology

Homology cylinders: an enlargement of the mapping class group

Jerome Levine

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.

Article information

Source
Algebr. Geom. Topol., Volume 1, Number 1 (2001), 243-270.

Dates
Accepted: 17 April 2001
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.agt/1513882592

Digital Object Identifier
doi:10.2140/agt.2001.1.243

Mathematical Reviews number (MathSciNet)
MR1823501

Zentralblatt MATH identifier
0978.57015

Citation

Levine, Jerome. Homology cylinders: an enlargement of the mapping class group. Algebr. Geom. Topol. 1 (2001), no. 1, 243--270. doi:10.2140/agt.2001.1.243. https://projecteuclid.org/euclid.agt/1513882592

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