Translator Disclaimer
2001 Homology cylinders: an enlargement of the mapping class group
Jerome Levine
Algebr. Geom. Topol. 1(1): 243-270 (2001). DOI: 10.2140/agt.2001.1.243

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.

Citation

Download Citation

Jerome Levine. "Homology cylinders: an enlargement of the mapping class group." Algebr. Geom. Topol. 1 (1) 243 - 270, 2001. https://doi.org/10.2140/agt.2001.1.243

Information

Received: 14 November 2000; Accepted: 17 April 2001; Published: 2001
First available in Project Euclid: 21 December 2017

zbMATH: 0978.57015
MathSciNet: MR1823501
Digital Object Identifier: 10.2140/agt.2001.1.243

Subjects:
Primary: 57N10
Secondary: 57M25

Rights: Copyright © 2001 Mathematical Sciences Publishers

JOURNAL ARTICLE
28 PAGES


SHARE
Vol.1 • No. 1 • 2001
MSP
Back to Top