Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Order One Invariants of Immersions   We classify all order one invariants of immersions of a closed orientable
surface F into R^3, with values in an arbitrary Abelian group G. We show that
for any F and G and any regular homotopy class A of immersions of F into R^3,
the group of all order one invariants on A is isomorphic to G^\aleph_0 \oplus B
\oplus B where G^\aleph_0 is the group of all functions from a set of
cardinality \aleph_0 into G and B={x\in G : 2x=0}. Our work includes
foundations for the study of finite order invariants of immersions of a closed
orientable surface into R^3, analogous to chord diagrams and the 1-term and
4-term relations of knot theory.

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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph