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 [IK]. Furthermore, we give an algorithm to algebraically describe the fundamental 3-class of any hyperbolic knot.
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