Encomplexing the writhe

Details Encomplexing the writhe Encomplexing the writhe

2000-05-16

arxiv.org/abs/math/0005162v1

Mathematics

Algebraic Geometry

17 pages, 4 figures, will appear in the Rokhlin memorial AMS volume

Scientific paper

A detailed version of preprint "Self-linking number of a real algebraic link" by the same author, alg-geom/9410030. For a nonsingular real algebraic curve in 3-dimensional projective space or 3-sphere, a new integer-valued characteristic is introduced. It is invariant under rigid isotopy and multiplied by -1 under mirror reflections. In a sense, it is a Vassiliev invariant of degree 1 and a counterpart of a link diagram writhe. For a regular complete intersection this invariant vanishes, while for rational knots of degree d it takes all the values between -(d-1)(d-2)/2 and (d-1)(d-2)/2.

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