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
Scholar Commons Citation
Clark, W. Edwin; Dunning, Larry A.; and Saito, Masahico, "Computations of Quandle 2-cocycle knot Invariants Without Explicit 2-cocycles" (2017). Mathematics and Statistics Faculty Publications. 105.
https://digitalcommons.usf.edu/mth_facpub/105
