A Transcendental Invariant of Pseudo-Anosov Maps

Hongbin Sun

doi:10.1112/jtopol/jtv010

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arXiv · 1209.2613

A Transcendental Invariant of Pseudo-Anosov Maps

Hongbin Sun

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Abstract

For each pseudo-Anosov map $ϕ$ on surface $S$, we will associate it with a $\mathbb{Q}$-submodule of $\mathbb{R}$, denoted by $A(S,ϕ)$. $A(S,ϕ)$ is defined by an interaction between the Thurston norm and dilatation of pseudo-Anosov maps. We will develop a few nice properties of $A(S,ϕ)$ and give a few examples to show that $A(S,ϕ)$ is a nontrivial invariant. These nontrivial examples give an answer to a question asked by McMullen: the minimal point of the restriction of the dilatation function on fibered face need not be a rational point.

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BibTeX RIS

Hongbin Sun. 2013-05-09. A Transcendental Invariant of Pseudo-Anosov Maps. https://doi.org/10.1112/jtopol%2Fjtv010

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