Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semisimple actions of mapping class groups on CAT(0) spaces   Let S be an orientable surface of finite type and let Mod(S) be its mapping
class group. We consider actions of Mod(S) by semisimple isometries on complete
CAT(0) spaces. If the genus of S is at least 3, then in any such action all
Dehn twists act as elliptic isometries. The action of Mod(S) on the completion
of Teichm\"uller space with the Weil-Petersson metric shows that there are
interesting actions of this type.
  Whenever the mapping class group of a closed orientable surface of genus g
acts by semisimple isometries on a complete CAT(0) space of dimension less than
g it must fix a point.
  The mapping class group of a closed surface of genus 2 acts properly by
semisimple isometries on a complete CAT(0) space of dimension 18.

6
The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
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The categories of this paper are: physics