On Alexander-Conway Polynomials for Virtual Knots and Links

Abstract

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.

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

Cited by in corpus (29)

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• Milnor's concordance invariants for knots on surfaces
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• Alexander invariants of periodic virtual knots
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• Virtual Braids and the L--Move
• Virtual Knot Theory --Unsolved Problems
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• Double coverings of twisted links
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• Relating virtual knot invariants to links in ${\mathbb{S}}^3$
• Virtual links which are equivalent as twisted links
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• On arrow polynomials of checkerboard colorable virtual links