On the fundamental 3-classes of knot group representations

2016/09/19 by Takefumi Nosaka, Nosaka, Takefumi
Mathematics · Medicine · #Algebraic Topology (math.AT) #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1609.05766

openalex publication_date 2016/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \citeIK. Furthermore, we give an algorithm to algebraically describe the fundamental 3-class of any hyperbolic knot.

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