Minimal Entropy of $3$-manifolds

Erika Pieroni

Minimal Entropy of $3$-manifolds

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arxiv 1902.09190 v1 pith:RURJKIGL submitted 2019-02-25 math.DG math.GTmath.MG

Erika Pieroni This is my paper · ORCID

classification math.DGmath.GTmath.MG

keywords minimalentropycubemanifoldscloseddecompositionorientableprime

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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.

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Topological volumes of certain complete affine manifolds
math.GT 2025-02 accept novelty 6.0 of 10

Complete affine manifolds with an infinite amenable normal subgroup have amenable category at most their dimension, so all three topological volumes vanish.

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