Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From Hierarchical to Relative Hyperbolicity   We provide a simple, combinatorial criteria for a hierarchically hyperbolic
space to be relatively hyperbolic by proving a new formulation of relative
hyperbolicity in terms of hierarchy structures. In the case of clean
hierarchically hyperbolic groups, this criteria characterizes relative
hyperbolicity. We apply our criteria to graphs associated to surfaces and prove
that the separating curve graph of a surface is relatively hyperbolic when the
surface has zero or two punctures. We also recover a celebrated theorem of
Brock and Masur on the relative hyperbolicity of the Weil-Petersson metric on
Teichmuller space for surfaces with complexity three.

23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg