Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pseudo-Anosovs optimizing the ratio of Teichm\"uller to curve graph
  translation length   Given $\phi$ a pseudo-Anosov map, let $\ell_\mathcal{T}(\phi)$ denote the
translation length of $\phi$ in the Teichm\"uller space, and let
$\ell_\mathcal{C}(\phi)$ denote the stable translation length of $\phi$ in the
curve graph. Gadre--Hironaka--Kent--Leininger showed that, as a function of
Euler characteristic $\chi(S)$, the minimal possible ratio $\tau(\phi) =
\frac{\ell_\mathcal{T}(\phi)}{\ell_\mathcal{C}(\phi)}$ is $\log(|\chi(S)|)$, up
to uniform additive and multiplicative constants. In this short note, we
introduce a new construction of such ratio optimizers and demonstrate their
abundance in the mapping class group. Further, we show that ratio optimizers
can be found arbitrarily deep into the Johnson filtration as well as in the
point pushing subgroup.

20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio