2000/05/16 by Oleg Viro, Viro, Oleg
Mathematics · #14H99 #14P25 #57M25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AG #math.GT #msc:14H99 #msc:14P25 #msc:57M25
paper · pdf · doi:10.48550/arxiv.math/0005162
17 pages, 4 figures, will appear in the Rokhlin memorial AMS volume
arxiv created 2000/05/16 · openalex publication_date 2000/05/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.