Title

Longitudinal Mapping Knot Invariant for SU(2)

Document Type

Article

Publication Date

2018

Keywords

Quandle, knot coloring polynomial, quandle cocycle invariant, SU(2)

Digital Object Identifier (DOI)

https://doi.org/10.1142/S0218216518430149

Abstract

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).

Was this content written or created while at USF?

Yes

Citation / Publisher Attribution

Journal of Knot Theory and Its Ramifications, v. 27, issue 11, art. 1843014

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