#### 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.

Notes on file formats
Takuro Mochizuki

Department of Mathematics, Kyoto University

Kyoto, 606--8502, Japan

Email: takuro@math.kyoto-u.ac.jp

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