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• W2963629440 abstract "We explore a knot invariant derived from colorings of corresponding [Formula: see text]-tangles with arbitrary connected quandles. When the quandle is an abelian extension of a certain type the invariant is equivalent to the quandle [Formula: see text]-cocycle invariant. We construct many such abelian extensions using generalized Alexander quandles without explicitly finding [Formula: see text]-cocycles. This permits the construction of many [Formula: see text]-cocycle invariants without exhibiting explicit [Formula: see text]-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 [Formula: see text]-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." @default.
• W2963629440 created "2019-07-30" @default.
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• W2963629440 date "2017-02-24" @default.
• W2963629440 modified "2023-09-24" @default.
• W2963629440 title "Computations of quandle 2-cocycle knot invariants without explicit 2-cocycles" @default.
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• W2963629440 doi "https://doi.org/10.1142/s0218216517500353" @default.
• W2963629440 hasPubMedCentralId "https://www.ncbi.nlm.nih.gov/pmc/articles/8023396" @default.
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