Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complex Hyperbolic Structures on Disc Bundles over Surfaces   We study complex hyperbolic disc bundles over closed orientable surfaces that
arise from discrete and faithful representations H_n->PU(2,1), where H_n is the
fundamental group of the orbifold S^2(2,...,2) and thus contains a surface
group as a subgroup of index 2 or 4. The results obtained provide the first
complex hyperbolic disc bundles M->{\Sigma} that: admit both real and complex
hyperbolic structures; satisfy the equality 2(\chi+e)=3\tau; satisfy the
inequality \chi/2<e; and induce discrete and faithful representations
\pi_1\Sigma->PU(2,1) with fractional Toledo invariant; where {\chi} is the
Euler characteristic of \Sigma, e denotes the Euler number of M, and {\tau}
stands for the Toledo invariant of M. To get a satisfactory explanation of the
equality 2(\chi+e)=3\tau, we conjecture that there exists a holomorphic section
in all our examples.
  In order to reduce the amount of calculations, we systematically explore
coordinate-free methods.

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The categories of this paper are: eess
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga