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Addendum and correction to: “Homology cylinders: an enlargement of the mapping class group”

Jerome Levine

Algebraic & Geometric Topology 2 (2002) 1197–1204

DOI: 10.2140/agt.2002.2.1197

Correction to Algebraic & Geometric Topology 1 (2001) 243–270

arXiv: math.GT/0207290
Abstract

In a previous paper [Homology cylinders: an enlargement of the mapping class group, Algebr. Geom. Topol. 1 (2001) 243–270], a group Hg of homology cylinders over the oriented surface of genus g is defined. A filtration of Hg is defined, using the Goussarov-Habiro notion of finite-type. It is erroneously claimed that this filtration essentially coincides with the relative weight filtration. The present note corrects this error and studies the actual relation between the two filtrations.

Keywords

homology cylinder, mapping class group
Mathematical Subject Classification

Primary: 57N10

Secondary: 57M25
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Publication

Received: 5 August 2002
Accepted: 17 December 2002
Published: 27 December 2002
Authors
Jerome Levine
Department of Mathematics
Brandeis University
Waltham MA 02454-9110
USA
http://people.brandeis.edu/~levine/