Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higgs bundles, the Toledo invariant and the Cayley correspondence   We define the Toledo invariant of a G-Higgs bundle on a Riemann surface,
where G is a real semisimple group of Hermitian type, and we prove a
Milnor-Wood type bound for this invariant when the bundle is semistable.
  We prove rigidity results when the Toledo invariant is maximal, establishing
in particular a Cayley correspondence when the symmetric space defined by G is
of tube type.
  This gives a new proof of the Milnor-Wood inequality of Burger-Iozzi-Wienhard
for representations of the fundamental group of a Riemann surface into G.
Compared to previous results using Higgs bundles, it uses general theory and
avoids any case by case study.

36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org