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 2017ons and related topics. The book is written from topological aspects, but it illustrates how esteemed quandle theory is in mathematics, and it constitutes a crash course for studying quandles..More precisely, this work emphasizes the fresh perspective that quandle theory can be useful for the study

等待

Some of Quandle Cocycle Invariants of Links,o a shadow version, a non-abelian one, and a bigraded one (see Sects. .–. respectively). In this chapter, we study the invariants with various versions in turn. We assume basic knowledge of CW-complexes (see the textbook [Hat]).

柱廊

Topology of the Rack Space and the 2-Cocycle Invariant, ., we give some examples. The reader who is interested only in the cocycle invariants may safely skip to Chap. .. .. In this chapter, by . we always mean a quandle, and by .(.) we do the connected components of ..

FLAX

,Inoue–Kabaya Chain Map,ns (in particular, the fundamental 3-class). After that, following the outline and philosophy, we describe concrete applications. To be precise, in Sect. ., we recover the Chern-Simons invariants of hyperbolic links, and in Sect. ., we will reconsider the bilinear cohomology pairings of links.

完全

,-Colorings of Links,and list some examples with applications. In Sect. ., we briefly observe a relation between colorings and the braid group. Here, we assume that the reader has the elementary knowledge in knot theory (for this, we refer the reader to the books [Hil,Lic, BZ] or Appendix A).

Spangle

Topology on the Quandle Homotopy Invariant,group homology. After that, in Sect. ., we discuss the homotopy type of the rack space of the link quandle; In Sect. ., we give a topological meaning of the quandle homotopy link-invariant. Finally, we provide a method of computing the third quandle homology; see Sect. ..

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笨拙的你

,-Colorings of Links,e knot quandle. Precisely, in Sect. ., we define colorings and observe examples. In Sect.  ., we see a topological characterization of the colorings, and list some examples with applications. In Sect. ., we briefly observe a relation between colorings and the braid group. Here, we assume that the re

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Some of Quandle Cocycle Invariants of Links,uced by Fenn-Rourke-Sanderson [FRS1, FRS2], and is graded by a homotopy group. After that, from the homological viewpoints, Carter-Jelsovsky-Kamada-Langford-Saito [CJKLS] used quandle cocycles to introduce computable link-invariants (which are called .). Furthermore, the invariants are generalized t

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