Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Property FW and 1-dimensional piecewise groups   Property FW is a natural combinatorial weakening of Kazhdan's Property T. We
prove that the group of piecewise homographic self-transformations of the real
projective line, has "few" infinite subgroups with Property FW. In particular,
no such subgroup is amenable or has Kazhdan's Property T. These results are
extracted from a longer paper. We provide a complete proof, whose main tools
are the use of the notion of partial action and of one-dimensional geometric
structures.

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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: stat