Longitudinal Mapping Knot Invariant for SU(2)
Quandle, knot coloring polynomial, quandle cocycle invariant, SU(2)
Digital Object Identifier (DOI)
The knot coloring polynomial defined by Eisermann for a finite pointed group is generalized to an infinite pointed group as the longitudinal mapping invariant of a knot. In turn, this can be thought of as a generalization of the quandle 2-cocycle invariant for finite quandles. If the group is a topological group, then this invariant can be thought of as a topological generalization of the 2-cocycle invariant. The longitudinal mapping invariant is based on a meridian–longitude pair in the knot group. We also give an interpretation of the invariant in terms of quandle colorings of a 1-tangle for generalized Alexander quandles without use of a meridian–longitude pair in the knot group. The invariant values are concretely evaluated for the torus knots T(2,n), their mirror images, and the figure eight knot for the group SU(2).
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Citation / Publisher Attribution
Journal of Knot Theory and Its Ramifications, v. 27, issue 11, art. 1843014
Scholar Commons Citation
Clark, W. Edwin and Saito, Masahico, "Longitudinal Mapping Knot Invariant for SU(2)" (2018). Mathematics and Statistics Faculty Publications. 101.