In a previous paper [Homology cylinders: an enlargement of the mapping class group, Algebr. Geom. Topol. 1 (2001) 243–270], a group of homology cylinders over the oriented surface of genus is defined. A filtration of 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.
"Addendum and correction to: “Homology cylinders: an enlargement of the mapping class group”." Algebr. Geom. Topol. 2 (2) 1197 - 1204, 2002. https://doi.org/10.2140/agt.2002.2.1197