On Alexander-Conway Polynomials for Virtual Knots and Links

Details On Alexander-Conway Polynomials for Virtual Knots and Links On Alexander-Conway Polynomials for Virtual Knots and Links

1999-12-21

arxiv.org/abs/math/9912173v2

Mathematics

Geometric Topology

17 pages, 11 figures, latex2e, metafont; error in example corrected and minor changes

Scientific paper

A polynomial invariant of virtual links, arising from an invariant of links in thickened surfaces introduced by Jaeger, Kauffman, and Saleur, is defined and its properties are investigated. Examples are given that the invariant can detect chirality and even non-invertibility of virtual knots and links. Furthermore, it is shown that the polynomial satisfies a Conway-type skein relation - in contrast to the Alexander polynomial derived from the virtual link group.

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