Algebraic and Geometric Topology 5 (2005), paper no. 10, pages 183-205.

The 3-cocycles of the Alexander quandles F_q[T]/(T-omega)

Takuro Mochizuki

Abstract. We determine the third cohomology of Alexander quandles of the form F_q[T]/(T-omega), where F_q denotes the finite field of order q and omega is an element of F-q which is neither 0 nor 1. As a result, we obtain many concrete examples of non-trivial 3-cocycles.

Keywords. Quandle, cohomology, knot

AMS subject classification. Primary: 18H40. Secondary: 55A25, 57Q45.

DOI: 10.2140/agt.2005.5.183

E-print: arXiv:math.GT/0210419

Submitted: 31 May 2004. Accepted: 21 September 2004. Published: 23 March 2005.

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Takuro Mochizuki
Department of Mathematics, Kyoto University
Kyoto, 606--8502, Japan
Email: takuro@math.kyoto-u.ac.jp

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