Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graphs of curves and arcs quasi-isometric to big mapping class groups   Following the work of Rosendal and Mann and Rafi, we try to answer the
following question: when is the mapping class group of an infinite-type surface
quasi-isometric to a graph whose vertices are curves on that surface? With the
assumption of tameness as defined by Mann and Rafi, we describe a necessary and
sufficient condition, called translatability, for a geometrically nontrivial
big mapping class group to admit such a quasi-isometry. In addition, we show
that the mapping class group of the plane minus a Cantor set is quasi-isometric
to the loop graph defined by Bavard, which we believe represents the first
example of a mapping class group known to be non-elementary hyperbolic.

24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio