Volume 5, issue 1 (2005)

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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
 arXiv: math.GT/0210419
Abstract

We determine the third cohomology of Alexander quandles of the form ${\mathbb{F}}_{q}\left[T\right]∕\left(T-\omega \right)$, where ${\mathbb{F}}_{q}$ denotes the finite field of order $q$ and $\omega$ is an element of ${\mathbb{F}}_{q}$ 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