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A Study of Braids (Paperback, Softcover reprint of hardcover 1st ed. 1999)
Loot Price: R1,530
Discovery Miles 15 300
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A Study of Braids (Paperback, Softcover reprint of hardcover 1st ed. 1999)
Series: Mathematics and Its Applications, 484
Expected to ship within 10 - 15 working days
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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] , that is a surprising application of
braid theory to the theory of algebraic equations.
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