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Titlebook: A Study of Braids; Kunio Murasugi,Bohdan I. Kurpita Book 1999 Springer Science+Business Media Dordrecht 1999 Group theory.Homotopy.Mathema

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期刊全稱A Study of Braids
影響因子2023Kunio Murasugi,Bohdan I. Kurpita
視頻videohttp://file.papertrans.cn/143/142291/142291.mp4
學(xué)科分類Mathematics and Its Applications
圖書封面Titlebook: A Study of Braids;  Kunio Murasugi,Bohdan I. Kurpita Book 1999 Springer Science+Business Media Dordrecht 1999 Group theory.Homotopy.Mathema
影響因子In Chapter 6, we describe the concept of braid equivalence from the topological point of view. This will lead us to a new concept braid homotopy that is discussed fully in the next chapter. As just mentioned, in Chapter 7, we shall discuss the difference between braid equivalence and braid homotopy. Also in this chapter, we define a homotopy braid invariant that turns out to be the so-called Milnor number. Chapter 8 is a quick review of knot theory, including Alexander‘s theorem. While, Chapters 9 is devoted to Markov‘s theorem, which allows the application of this theory to other fields. This was one of the motivations Artin had in mind when he began studying braid theory. In Chapter 10, we discuss the primary applications of braid theory to knot theory, including the introduction of the most important invariants of knot theory, the Alexander polynomial and the Jones polynomial. In Chapter 11, motivated by Dirac‘s string problem, the ordinary braid group is generalized to the braid groups of various surfaces. We discuss these groups from an intuitive and diagrammatic point of view. In the last short chapter 12, we present without proof one theorem, due to Gorin and Lin [GoL] , tha
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Quotient groups of the braid group,of tourism over time. A third section covers the history of post-World War II interventions and efforts to tie heritage sites to economic development. The chapter further treats the changing tourist population and the growth of other types of tourist venues, and finally looks at the emergence of new
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Isotopy of braids,ines two sites where tourism and visitor development have been critical: the Falkirk Wheel (the site of a mature visitor attraction and related facilities) and the Helix Park (the site of the iconic Kelpie sculptures). Such contrasting sites provide a unique opportunity to consider development, oper
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,Markov’s theorem,authors engage the multiple scales at which heritage works, from the vernacular to official and from the forgotten to the famous World Heritage List and into cyberspace. And they consider the many ethical challenges attendant to heritage. We examine the expediency of heritage and the complex ways in
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Knot invariants,th European interest in preservation and restoration, did, however, lay the foundation for protecting heritage as a value in itself. Thus, even though restricted to national monuments, the preservation movements of the nineteenth century initiated the discussion that would lead to making national ar
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