Lipschitz Simplicial Volume of Connected Sums

TL;DR

This paper establishes the additivity of locally finite and Lipschitz simplicial volumes under specific manifold gluings, especially connected sums in dimensions three and higher, involving boundary components with certain properties.

Contribution

It proves the additivity of these volumes under connected sums and gluings along boundary components with amenable aspherical fundamental groups.

Findings

Additivity of simplicial volumes under connected sums in dimension ≥ 3

Additivity with respect to gluings along π₁-injective, amenable aspherical boundaries

Extension of simplicial volume properties to new classes of manifold gluings

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 $\geq 3$ they are additive with respect to connected sums and gluings along $\pi_1$-injective, amenable aspherical boundary components.