Titlebook: Knot Theory and Its Applications; Kunio Murasugi Textbook 1996 Springer Science+Business Media New York 1996 Algebraic topology.Knot invar

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Knot Theory and Its Applications978-0-8176-4719-3Series ISSN 2197-1803 Series E-ISSN 2197-1811

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The Jones Revolution,Alexander polynomial, the signature of a knot, ., V. Jones announced the discovery of a new invariant. Instead of further propagating pure theory in knot theory, this new invariant and its subsequent offshoots unlocked connections to various applicable disciplines, some of which we will discuss in the subsequent chapters.

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Fundamental Problems of Knot Theory,The problems that arise when we study the theory of knots can essentially be divided into two types. On the one hand, there are those that we shall call ., while, in contrast, there are those that we shall call ..

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Vassiliev Invariants,Towards the end of the 1980s in the midst of the Jones revolution, V.A. Vassiliev introduced a new concept that has had profound significance in the immediate aftermath of the Jones revolution in knot theory [V]. The importance of these so-called Vassiliev invariants lies in that they may be used to study Jones-type invariants more systematically.

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Creating Manifolds from Knots, of manifolds (see Definition 8.0.1 below). In this chapter we will show that it is possible to create from an arbitrary knot (or link) a 3-dimensional manifold (usually shortened to 3-manifold). Hence by studying the properties of knots we can gain insight into the properties of 3-manifolds.

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