Volume 5, issue 1 (2005)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The 3–cocycles of the Alexander quandles $\mathbb{F}_q[T]/(T-\omega)$

Takuro Mochizuki

Algebraic & Geometric Topology 5 (2005) 183–205

arXiv: math.GT/0210419

Abstract

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

Keywords
quandle, cohomology, knot
Mathematical Subject Classification 2000
Primary: 18G60
Secondary: 55N35, 57Q45
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Publication
Received: 31 May 2004
Accepted: 21 September 2004
Published: 23 March 2005
Authors
Takuro Mochizuki
Department of Mathematics
Kyoto University
Kyoto
606–8502
Japan