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

Abstract

In a previous paper [Homology cylinders: an enlargement of the mapping class group, Algebr. Geom. Topol. 1 (2001) 243–270], a group ${\mathcal{\mathscr{H}}}_g$ of homology cylinders over the oriented surface of genus $g$ is defined. A filtration of ${\mathcal{\mathscr{H}}}_g$ 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.