Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Torsion Invariants of Combed 3-Manifolds with Boundary Pattern and
  Legendrian Links   We extend Turaev's definition of torsion invariants of 3-dimensional
manifolds equipped with non-singular vector fields, by allowing (suitable)
tangency circles to the boundary, and manifolds with non-zero Euler
characteristic. We show that these invariants apply in particular to (the
exterior of) Legendrian links in contact 3-manifolds. Our approach uses a
combinatorial encoding of vector fields, based on standard spines. In this
paper we extend this encoding from closed manifolds to manifolds with boundary.

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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph