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Abstract: A few years ago V.I.Arnold applied Vassiliev's philosophy of finite
type invariants to the theory of immersed plane curves. He discovered that
the discriminant of a non-generic immersed plane curve has three
components which he called J^+, J^-, and St. Treating these
components separately we get three different theories.
Arnold showed that J^+ and J^- theories lead to the theory of
Legendrian knots in a solid torus, hence they contain the ordinary
topological knot theory. It turns out that the
"strangeness" theory St is trivial in a sense that there exists a
complete combinatorial invariant for determining the strangeness
equivalence.
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