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# 数学代写|扭结理论代写Knot Theory代考|MATH5801 A Brief Introduction to Hyperbolic Knots

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## 数学代写|扭结理论代写Knot Theory代考|A Brief Introduction to Hyperbolic Knots

This book gives an introduction to knots, links, and hyperbolic geometry. Before we begin, we need to carefully define what we mean by knots and links, and that is done in this chapter. We also introduce classical problems in knot theory, and problems motivated by geometry, especially hyperbolic geometry. This chapter is meant to motivate future chapters, and it has many references to content covered in more detail later in the book, where we address some of these problems. Many of the questions described in this chapter have partial answers, and many are still wide open.

## 数学代写|扭结理论代写Knot Theory代考|An introduction to knot theory

The earliest study of knots seems to be by Gauss, Listing, and especially Tait, who published several papers on knot theory in the years 1876 through 1885. In a preface to his work on knot theory, republished in his 1898 Scientific papers [Tai98], Tait writes:
“The subject [knot theory] is a very much more difficult and intricate one than at first sight one is inclined to think, and I feel that I have not succeeded in catching the keynote.”
Since Tait’s work, advances in knot theory have come through applications of topology, algebra, and invariants arising in quantum field theory, but no single mathematical field has led to simple tools that apply to all knots. In other words, perhaps mathematicians still have not succeeded in catching the “key-note.” Perhaps there is no “key-note” in knot theory.

However, there are definitely mathematical techniques that work well when applied to particular problems or particular families. This book introduces techniques arising from geometry.

## 数学代写|扭结理论代写Knot Theory代考|An introduction to knot theory

“这个主题 [结理论] 比乍一看的人倾向于认为的要困难和复杂得多，我觉得我没有成功抓住主题。”

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