Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Sequence of Degree One Vassiliev Invariants for Virtual Knots   For ordinary knots in R3, there are no degree one Vassiliev invariants. For
virtual knots, however, the space of degree one Vassiliev invariants is
infinite dimensional. We introduce a sequence of three degree one Vassiliev
invariants of virtual knots of increasing strength. We demonstrate that the
strongest invariant is a universal Vassiliev invariant of degree one for
virtual knots in the sense that any other degree one Vassiliev invariant can be
recovered from it by a certain natural construction. To prove these results, we
extend the based matrix invariant introduced by Turaev for virtual strings to
the class of singular virtual knots with one double-point.

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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat