#### Volume 2, issue 2 (2002)

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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
 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 ${\mathsc{ℋ}}_{g}$ of homology cylinders over the oriented surface of genus $g$ is defined. A filtration of ${\mathsc{ℋ}}_{g}$ 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
Primary: 57N10
Secondary: 57M25