書籍詳細

書籍詳細




洋書

伊藤昇(共)著/結び目の射影

Knot Projections

Ito, Noboru

Chapman & Hall 2016/12
200 p. 50 illus. 24 cm   
装丁: Hrd    装丁について
テキストの言語: ENG    出版国: GB
ISBN: 9781498736756
KCN: 1024193937
紀伊國屋書店 選定タイトル
標準価格:¥12,119(本体 ¥11,018)   
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納期について
DDC: 516
KDC: F15 位相幾何学
書評掲載: Choice Reviews 2017 August
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Annotation

The book gives an overview of methods to study knot projections. The intuitiveness of the objects allows us to present current research to audiences with a general mathematical background without requiring any knowledge of special (topology) courses. The book can be taken as a first approach to topology, alternative to the one given by standard text books. Exercises will be included. Nevertheless, it is mainly an introduction to an active research area, including many open questions.

Full Description

Knot Projections offers a comprehensive overview of the latest methods in the study of this branch of topology, based on current research inspired by Arnold's theory of plane curves, Viro's quantization of the Arnold invariant, and Vassiliev's theory of knots, among others. The presentation exploits the intuitiveness of knot projections to introduce the material to an audience without a prior background in topology, making the book suitable as a useful alternative to standard textbooks on the subject. However, the main aim is to serve as an introduction to an active research subject, and includes many open questions.

Table of Contents

Introduction. Mathematical Background. A topological invariant of knot projections. Classification by RI and RII. Classification by strong and weak RIII. Constructing new topological invariants of equivalence classes of knot projections. Survey on classification problems of knot projections.