On the fundamental 3-classes of knot group representations

Takefumi Nosaka

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arXiv · 1609.05766

On the fundamental 3-classes of knot group representations

Takefumi Nosaka

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Abstract

We discuss the fundamental (relative) 3-classes of knots (or hyperbolic links), and provide diagrammatic descriptions of the push-forwards with respect to every link-group representation. The point is an observation of a bridge between the relative group homology and quandle homology from the viewpoints of Inoue--Kabaya map \cite{IK}. Furthermore, we give an algorithm to algebraically describe the fundamental 3-class of any hyperbolic knot.

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Takefumi Nosaka. 2016-09-19. On the fundamental 3-classes of knot group representations. https://arxiv.org/abs/1609.05766

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