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arxiv: 0704.3995 · v1 · submitted 2007-04-30 · 🧮 math.GT

Polynomial cocycles of Alexander quandles and applications

classification 🧮 math.GT
keywords quandlequandlesalexanderapplicationscocyclesgroupshomologynon-triviality
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Cocycles are constructed by polynomial expressions for Alexander quandles. As applications, non-triviality of some quandle homology groups are proved, and quandle cocycle invariants of knots are studied. In particular, for an infinite family of quandles, the non-triviality of quandle homology groups is proved for all odd dimensions.

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