Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Veech groups without parabolic elements   We prove that a ``bouillabaisse'' surface (translation surface which has two
transverse parabolic elements) has totally real trace field. As a corollary,
non trivial Veech groups which have no parabolic elements do exist. The proof
follows Veech's viewpoint on Thurston's construction of pseudo-Anosov
diffeomorphisms.

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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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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: comp-gas
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The categories of this paper are: hep-ex