Minimal Entropy of $3$-manifolds

Abstract

We compute the Minimal Entropy of every closed, orientable $3$-manifold, showing that its cube equals the sum of the cubes of the minimal entropies of each hyperbolic component arising from the $JSJ$ decomposition of each prime summand. As a consequence we show that the cube of the Minimal Entropy is additive with respect to both the prime and the $JSJ$ decomposition, thus concluding that for closed orientable $3$-manifolds the cube of the Minimal Entropy is proportional to the simplicity volume. This answers a conjecture asked by Anderson and Paternain for irreducible manifolds.

arXiv comment96pp, 9 figures. This thesis has been typeset using sapthesis class. PhD Thesis defended on 18th January 2019 at Sapienza, University of Rome. Advisor: Andrea Sambusetti (Sapienza, Roma). Board of examiners: Roberto Frigerio (Università di Pisa), Alessandro Savo (Sapienza, Roma), Juan Souto (CNRS, Université Rennes I)

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Cited by in corpus (4)

• Minimal volume entropy of simplicial complexes
• Topological volumes of fibrations: A note on open covers
• Minimal volume entropy and fiber growth
• Essential minimal volume of Einstein 4-manifolds