On the (super)additivity of simplicial volume

Abstract

We show that the simplicial volume is superadditive with respect to gluings along certain submanifolds of the boundary. Our criterion applies to boundary connected sums and 1-handle attachments. Moreover, we generalize a well-known additivity result in the case of aspherical manifolds. Our arguments are based on new results about relative bounded cohomology and pairs of multicomplexes, which are of independent interest.

55 pages; completely rewritten; Lemma 3.6 in previous versions is false