Minimal volume entropy of mapping tori over 3-manifolds

2025/09/22 by Giuseppe Bargagnati, Alberto Casali, Bargagnati, Giuseppe +5 · 1 citation
Computer Science · #Topological and Geometric Data Analysis #Computer Graphics and Visualization Techniques #Computational Geometry and Mesh Generation

paper · pdf · doi:10.48550/arxiv.2509.17851

Abstract

We prove that the minimal volume entropy of mapping tori over oriented closed smooth 3-manifolds vanishes. Our approach uses a variation of the amenable category and a suitable version of the minimal volume entropy of a homology class introduced by Babenko and Sabourau.

Citations

• Amenable covers and integral foliated simplicial volume
• Minimal volume entropy and fiber growth
• Minimal volume entropy of free-by-cyclic groups and 2-dimensional\n right-angled Artin groups
• Minimal Entropy of 3-manifolds
• Bounded cohomology of discrete groups
• An Introduction to Geometric Topology
• Isometric Embeddings in Bounded Cohomology
• 3-manifold groups
• Homological invariance for asymptotic invariants and systolic inequalities
• The entropy formula for the Ricci flow and its geometric applications
• simplicial cohomology of orbifolds
• Homeomorphisms of 3-manifolds and the realization of Nielsen Number

Cited by

• On the integral simplicial volume of cyclic covers of mapping tori

Related

• Minimal Entropy of 3-manifolds
• The minimal entropy problem for 3-manifolds with zero simplicial volume
• Minimal Surface Entropy and Average Area Ratio
• Minimal volume entropy and fiber growth
• Topological entropy of minimal geodesics and volume growth on surfaces