Arnold-type Invariants of Curves on Surfaces

Details Arnold-type Invariants of Curves on Surfaces Arnold-type Invariants of Curves on Surfaces

1999-06-18

arxiv.org/abs/math/9906125v1

J. Knot Theory Ramifications 8 (1999), no. 1, pp. 71-97

Mathematics

Geometric Topology

25 pages, 11 figures

Scientific paper

Recently V. Arnold introduced Strangeness and $J^{\pm}$ invariants of generic
immersions of an oriented circle to $\R^2$. Here these invariants are
generalized to the case of generic immersions of an oriented circle to an
arbitrary surface $F$. We explicitly describe all the invariants satisfying
axioms, which naturally generalize the axioms used by V. Arnold.

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