Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Action of Thompson's Group on a CAT(0) Boundary   One way to show that Thompson's group F is non-amenable is to exhibit an
action of F on a locally compact CAT(0) space X containing no F-invariant flats
and having no global fixed points in its boundary-at-infinity. We study the
actions of Thompson's groups F, T, and V on the boundaries-at-infinity of
proper CAT(0) cubical complexes. In particular, we show that Thompson's groups
T and V act without fixing any points in the boundaries of their CAT(0) cubical
complexes. This in particular gives another proof of the well-known fact that
these groups are non-amenable. We obtain a partial description of the fixed set
for F: Thompson's group F fixes an arc in the boundary of its cubical complex.
We leave open the possibility that there are more fixed points, but describe a
region of the boundary which must contain all of the others.

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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat