English

Minimal Entropy of $3$-manifolds

Differential Geometry 2019-02-26 v1 Geometric Topology Metric Geometry

Abstract

We compute the Minimal Entropy of every closed, orientable 33-manifold, showing that its cube equals the sum of the cubes of the minimal entropies of each hyperbolic component arising from the JSJJSJ 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 JSJJSJ decomposition, thus concluding that for closed orientable 33-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.

Keywords

Cite

@article{arxiv.1902.09190,
  title  = {Minimal Entropy of $3$-manifolds},
  author = {Erika Pieroni},
  journal= {arXiv preprint arXiv:1902.09190},
  year   = {2019}
}

Comments

96pp, 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 (Universit\`a di Pisa), Alessandro Savo (Sapienza, Roma), Juan Souto (CNRS, Universit\'e Rennes I)