Entropy versus volume via Heegaard diagrams
Abstract
The following inequalities are established, improving a former inequality due to Kojima.For any closed arithmetic hyperbolic 3-manifold fibering over a circle, the entropy of the pseudo-Anosov monodromy is bounded by the hyperbolic volume of the 3-manifold, up to a universal constant factor.For any closed hyperbolic 3-manifold fibering over a circle with systole " > 0, the entropy is bounded by the hyperbolic volume times log.3C1="/, up to a universal constant factor.The proof relies on Heegaard Floer homology and hyperbolic geometry.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Geometric and Algebraic Topology
semigroups and automata theory
Publication details
- Journal / source
- Geometry & Topology
- Publisher
- Mathematical Sciences Publishers
- Volume
- 30
- Issue
- 4
- Pages
- 1515–1573
- Publication date
- 9 July 2026
- Language
- EN