Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orientations in Legendrian Contact Homology and Exact Lagrangian
  Immersions   We show how to orient moduli spaces of holomorphic disks with boundary on an
exact Lagrangian immersion of a spin manifold into complex n-space in a
coherent manner. This allows us to lift the coefficients of the contact
homology of Legendrian spin submanifolds of standard contact (2n+1)-space from
Z_2 to Z. We demonstrate how the Z-lift provides a more refined invariant of
Legendrian isotopy. We also apply contact homology to produce lower bounds on
double points of certain exact Lagrangian immersions into C^n and again
including orientations strengthens the results. More precisely, we prove that
the number of double points of an exact Lagrangian immersion of a closed
manifold M whose associated Legendrian embedding has good DGA is at least half
of the dimension of the homology of M with coefficients in an arbitrary field
if M is spin and in Z_2 otherwise.

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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: stat