Lipschitz Simplicial Volume of Connected Sums

Abstract

We prove that the locally finite simplicial volume and the Lipschitz simplicial volume are additive with respect to certain gluings of manifolds. In particular, we prove that in dimension $\ge 3$ they are additive with respect to connected sums and gluings along ${\pi }_1$-injective, amenable aspherical boundary components.

34 pages, 9 figures

References in corpus (1)

• Proportionality Principle for the Lipschitz simplicial volume

Cited by in corpus (1)

• Explicit ${\ell }^1$-efficient cycles and amenable normal subgroups