An Orientation-Sensitive Vassiliev Invariant for Virtual Knots

Details An Orientation-Sensitive Vassiliev Invariant for Virtual Knots An Orientation-Sensitive Vassiliev Invariant for Virtual Knots

2002-03-13

arxiv.org/abs/math/0203123v3

Mathematics

Geometric Topology

13 pages, 10 figures, latex2e, metafont; Corollary 6, Remarks and Example added, several corrections

Scientific paper

It is an open question whether there are Vassiliev invariants that can distinguish an oriented knot from its inverse, i.e., the knot with the opposite orientation. In this article, an example is given for a first order Vassiliev invariant that takes different values on a virtual knot and its inverse. The Vassiliev invariant is derived from the Conway polynomial for virtual knots. Furthermore, it is shown that the zeroth order Vassiliev invariant coming from the Conway polynomial cannot distinguish a virtual link from its inverse and that it vanishes for virtual knots.

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