Multicomplexes, bounded cohomology and additivity of simplicial volume
Thilo Kuessner
TL;DR
This paper investigates how the simplicial volume behaves under various boundary operations in manifolds, providing proofs for additivity and superadditivity in specific cases and exploring the doubling process in 3-manifolds.
Contribution
It offers new proofs of additivity and superadditivity of simplicial volume for manifolds with boundary, expanding understanding of its properties under boundary modifications.
Findings
Additivity of simplicial volume for glueing amenable boundary components
Superadditivity for glueing amenable submanifolds of the boundary
Discussion of doubling of 3-manifolds
Abstract
We discuss some additivity properties of the simplicial volume for manifolds with boundary: we give proofs of additivity for glueing amenable boundary components and of superadditivity for glueing amenable submanifolds of the boundary, and we discuss doubling of 3-manifolds.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Operator Algebra Research · Geometric Analysis and Curvature Flows