Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pseudo-Anosovs on closed surfaces having small entropy and the Whitehead
  sister link exterior   Let $\delta_g$ be the minimal dilatation for pseudo-Anosovs on a closed
surface $\Sigma_g$ of genus $g$ and let $\delta_g^+$ be the minimal dilatation
for pseudo-Anosovs on $\Sigma_g$ with orientable invariant foliations. This
paper concerns the pseudo-Anosovs which occur as the monodromies on closed
fibers for Dehn fillings of $N(r)$ for each $r \in \{-3/2, -1/2, 2\}$ of the
magic manifold $N$. The manifold $N(-3/2)$ is homeomorphic to the Whitehead
sister link exterior.
  We consider the set $\Lambda_g(r)$ (resp. $\Lambda_g^+(r)$) which consists of
the dilatations of all monodromies (resp. monodromies having orientable
invariant foliations) on a closed fiber of genus $g$ for Dehn fillings of
$N(r)$, where the fillings are on the boundary slopes of fibers of $N(r)$.
Hironaka obtained upper bounds of $\delta_g$ and $\delta_g^+$ by computing
$\min \Lambda_g(-1/2)$ and $\min \Lambda^+_g(-1/2)$ respectively. We prove that
$\min \Lambda_g(-3/2)< \min \Lambda_g(-1/2)$ for $g \equiv 0,1,5,6,7,9
\pmod{10}$ and $\min \Lambda^+_g(-3/2)< \min \Lambda^+_g(-1/2)$ for $g \equiv
1,5,7,9 \pmod{10}$. These inequalities improve the previous upper bounds of
$\delta_g$ and $\delta_g^+$ for these $g$.
  We prove that for each $r \in \{-3/2, -1/2, 2\}$ and each $g \ge 3$, there
exists a monodromy $\Phi_g(r)$ on a closed fiber of genus $g $ for a Dehn
filling of $N(r)$ such that its dilatation $\lambda(\Phi_g(r))$ satisfies
$\displaystyle \lim_{g \to \infty} |\chi(\Sigma_g)| \log \lambda (\Phi_g(r)) =
2 \log((3+\sqrt{5})/2)$.

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The categories of this paper are: adap-org
16
The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an