The 3–cocycles of the Alexander quandles 𝔽q[T]∕(T − ω)

Mochizuki, Takuro

doi:10.2140/agt.2005.5.183

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The 3–cocycles of the Alexander quandles $\mathbb{F}_q[T]/(T-\omega)$

Takuro Mochizuki

Algebraic & Geometric Topology 5 (2005) 183–205

DOI: 10.2140/agt.2005.5.183

arXiv: math.GT/0210419

Abstract

We determine the third cohomology of Alexander quandles of the form $F_{q} [T] ∕ (T - ω)$ , where $F_{q}$ denotes the finite field of order $q$ and $ω$ 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

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

Volume 5, issue 1 (2005)