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The multi-variable affine index polynomial. (English) Zbl 1435.57006
Summary: We define a multi-variable version of the affine index polynomial for virtual links. This invariant reduces to the original affine index polynomial in the case of virtual knots, and also generalizes the version for compatible virtual links recently developed by L. H. Kauffman [J. Knot Theory Ramifications 27, No. 11, Article ID 1843017, 29 p. (2018; Zbl 1436.57007)]. We prove that this invariant is a Vassiliev invariant of order one, and study what happens as we shift the coloring of one or more components.
MSC:
57K12 Generalized knots (virtual knots, welded knots, quandles, etc.)
57K14 Knot polynomials
57K16 Finite-type and quantum invariants, topological quantum field theories (TQFT)
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