✦ LIBER ✦

Knots and links

✍ Scribed by Dale Rolfsen

Book ID: 127456228
Publisher: American Mathematical Society
Year: 2003
Tongue: English
Weight: 5 MB
Series: AMS Chelsea Publishing
Edition: AMS
Category: Library
ISBN-13: 9780821834367

No coin nor oath required. For personal study only.

✦ Synopsis

Rolfsen's beautiful book on knots and links can be read by anyone, from beginner to expert, who wants to learn about knot theory. Beginners find an inviting introduction to the elements of topology, emphasizing the tools needed for understanding knots, the fundamental group and van Kampen's theorem, for example, which are then applied to concrete problems, such as computing knot groups. For experts, Rolfsen explains advanced topics, such as the connections between knot theory and surgery and how they are useful to understanding three-manifolds.

Besides providing a guide to understanding knot theory, the book offers "practical" training. After reading it, you will be able to do many things: compute presentations of knot groups, Alexander polynomials, and other invariants; perform surgery on three-manifolds; and visualize knots and their complements. It is characterized by its hands-on approach and emphasis on a visual, geometric understanding.

Rolfsen offers invaluable insight and strikes a perfect balance between giving technical details and offering informal explanations. The illustrations are superb, and a wealth of examples are included.

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## Abstract The main purpose of this paper is to show that any embedding of __K~7~__ in three‐dimensional euclidean space contains a knotted cycle. By a similar but simpler argument, it is also shown that any embedding of __K~6~__ contains a pair of disjoint cycles which are homologically linked.