Titlebook: Quandles and Topological Pairs; Symmetry, Knots, and Takefumi Nosaka Book 2017 The Author(s) 2017 Quandle.Relative objects.Low dimensional

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Book 2017ions of groups are discussed, e.g., spin structures, .K.2 groups,and some geometric anomalies. The third topic is a method to study relative information on a 3-dimensional manifold with a boundary, e.g., knot theory, relative cup products, and relative group cohomology..For applications in topology,

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Parameter

Takefumi NosakaShows how the quandle has been evaluated in relation to mathematics or topology while the quandle was often considered to be something combinatorial.Constitutes a guide on quandles at a time when few

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Relative Group Homology,ersion. After that, we give some examples, where the concept of malnormality is important. Furthermore, in Sect.?., we explicitly give some cocycles of relative group cohomology. Throughout this chapter, we represent a group by . and a right .-module by ..