Cubical simplicial volume of 3-manifolds
Clara Loeh, Cristina Pagliantini, Sebastian Waeber
TL;DR
This paper proves that for oriented closed 3-manifolds, the cubical simplicial volume is exactly one fifth of the traditional simplicial volume, establishing a precise quantitative relationship.
Contribution
It establishes a specific proportional relationship between cubical and ordinary simplicial volumes in 3-manifolds, a novel result in geometric topology.
Findings
Cubical simplicial volume equals one fifth of ordinary simplicial volume for 3-manifolds.
Provides a new explicit formula relating two types of simplicial volumes.
Advances understanding of volume invariants in geometric topology.
Abstract
We prove that cubical simplicial volume of oriented closed 3-manifolds is equal to one fifth of ordinary simplicial volume.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Geometry and complex manifolds