nLab
Vassiliev skein relation

The Vassiliev skein relation is a way to extend knot invariants to singular knots (at least, to singular knots where the only singularities are double points). If vv is a knot invariant that takes values in an abelian group, then it is extended to singular knots using the relation

v(L d)=v(L +)v(L ) v(L_d) = v(L_+) - v(L_-)

where L dL_d is a singular knot with a double point and L +L_+, respectively L L_-, are formed from L dL_d by replacing the double point by a positively oriented, respectively negatively oriented, crossing.

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\end{array}

category: knot theory

Revised on April 1, 2011 09:22:55 by Andrew Stacey (129.241.15.200)