On the fundamental 3-classes of knot group representations
| Autor: | Takefumi Nosaka |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Hyperbolic geometry 010102 general mathematics Geometric Topology (math.GT) Algebraic geometry Homology (mathematics) Mathematics::Geometric Topology 01 natural sciences Mathematics - Geometric Topology Diagrammatic reasoning Knot (unit) Differential geometry Knot group 0103 physical sciences FOS: Mathematics Algebraic Topology (math.AT) Mathematics - Algebraic Topology 010307 mathematical physics Geometry and Topology 0101 mathematics Projective geometry Mathematics |
| Zdroj: | Geometriae Dedicata. 204:1-24 |
| ISSN: | 1572-9168 0046-5755 |
| DOI: | 10.1007/s10711-019-00442-4 |
| Popis: | 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. 24 pages. I revised minor errors and some pictures. In Section 3, I rewrote the definition of the relative group homology, and described the chain map $\alpha$ |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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