Algebraic and Geometric Topology 2 (2002), paper no. 47, pages 1197-1204.

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

Jerome Levine

Abstract. In a previous paper [Homology cylinders: an enlargement of the mapping class group, Algebr. Geom. Topol. 1 (2001) 243--270, arXiv:math.GT/0010247], a group H_g of homology cylinders over the oriented surface of genus g is defined. A filtration of 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

AMS subject classification. Primary: 57N10. Secondary: 57M25.

DOI: 10.2140/agt.2002.2.1197

E-print: arXiv:math.GT/0207290

Submitted: 5 August 2002. Accepted: 17 December 2002. Published: 27 December 2002.

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Jerome Levine
Department of Mathematics, Brandeis University
Waltham, MA 02454-9110, USA
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