Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Word hyperbolic extensions of surface groups   Let S be a closed surface of genus at least 2. We show that a finitely
generated group G which is an extension of the fundamental group H of S is word
hyperbolic if and only the orbit map of the quotient group G/H on the complex
of curves is a quasi-isometric embedding.This in turn is equivalent to G/H
being convex cocompact in the sense of Farb and Mosher.

21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics