Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Transcendental Invariant of Pseudo-Anosov Maps   For each pseudo-Anosov map $\phi$ on surface $S$, we will associate it with a
$\mathbb{Q}$-submodule of $\mathbb{R}$, denoted by $A(S,\phi)$. $A(S,\phi)$ is
defined by an interaction between the Thurston norm and dilatation of
pseudo-Anosov maps. We will develop a few nice properties of $A(S,\phi)$ and
give a few examples to show that $A(S,\phi)$ 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.

27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph