Title

Computations of Quandle 2-cocycle knot Invariants Without Explicit 2-cocycles

Document Type

Article

Publication Date

2017

Keywords

Quandles, knot colorings, tangles, quandle cocycle invariants, abelian extensions of quandles

Digital Object Identifier (DOI)

https://doi.org/10.1142/S0218216517500353

Abstract

We explore a knot invariant derived from colorings of corresponding 1-tangles with arbitrary connected quandles. When the quandle is an abelian extension of a certain type the invariant is equivalent to the quandle 2-cocycle invariant. We construct many such abelian extensions using generalized Alexander quandles without explicitly finding 2-cocycles. This permits the construction of many 2-cocycles. We show that for connected generalized Alexander quandles the invariant is equivalent to Eisermann’s knot coloring polynomial. Computations using this technique show that the 2-cocycle invariant distinguishes all of the oriented prime knots up to 11 crossings and most oriented prime knots with 12 crossings including classification by symmetry: mirror images, reversals, and reversed mirrors.

Was this content written or created while at USF?

Yes

Citation / Publisher Attribution

Journal of Knot Theory and Its Ramifications, v. 26, issue 7, art. 1750035

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