Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On homotopy invariants of combings of 3-manifolds   Combings of oriented compact 3-manifolds are homotopy classes of nowhere zero
vector fields in these manifolds. A first known invariant of a combing is its
Euler class, that is the Euler class of the normal bundle to a combing
representative in the tangent bundle of the 3-manifold $M$. It only depends on
the Spin$^c$-structure represented by the combing. When this Euler class is a
torsion element of $H^2(M;Z)$, we say that the combing is a torsion combing.
Gompf introduced a $Q$-valued invariant $\theta_G$ of torsion combings of
closed 3-manifolds that distinguishes all combings that represent a given
Spin$^c$-structure. This invariant provides a grading of the Heegaard Floer
homology $\hat{HF}$ for manifolds equipped with torsion Spin$^c$-structures. We
give an alternative definition of the Gompf invariant and we express its
variation as a linking number. We also define a similar invariant $p_1$ for
combings of manifolds bounded by $S^2$. We show that the $\Theta$-invariant,
that is the simplest configuration space integral invariant of rational
homology spheres, is naturally an invariant of combings of rational homology
balls, that reads $(\frac14p_1 + 6 \lambda)$ where $\lambda$ is the
Casson-Walker invariant. The article also includes a mostly self-contained
presentation of combings.

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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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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: mtrl-th
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The categories of this paper are: patt-sol
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph