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Book

Knot Projections

Book

Knot Projections

DOI link for Knot Projections

Knot Projections book

Knot Projections

DOI link for Knot Projections

Knot Projections book

ByNoboru Ito
Edition 1st Edition
First Published 2016
eBook Published 1 November 2016
Pub. Location New York
Imprint Chapman and Hall/CRC
DOI https://doi.org/10.1201/9781315369570
Pages 220
eBook ISBN 9781315369570
Subjects Mathematics & Statistics
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Ito, N. (2016). Knot Projections (1st ed.). Chapman and Hall/CRC. https://doi.org/10.1201/9781315369570

ABSTRACT

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

chapter 1|6 pages

Knots, knot diagrams, and knot projections

chapter 2|10 pages

Mathematical background (1920s)

chapter 3|12 pages

Topological invariant of knot projections (1930s)

chapter 4|24 pages

Classification of knot projections under RI and RII (1990s)

chapter 5|20 pages

Classification by RI and strong orweak RII (1996– 2015)

chapter 6|22 pages

Techniques for counting sub-chord diagrams (2015–Future)

chapter 7|12 pages

Hagge–Yazinski Theorem (Necessity of RII)

chapter 8|14 pages

Further result of strong (1, 3) homotopy

chapter 9|34 pages

Half-twisted splice operations, reductivities, unavoidable sets, triple chords, and strong (1, 2) homotopy

chapter 10|22 pages

Weak (1, 2, 3) homotopy

chapter 11|22 pages

Viro’s quantization of Arnold invariant

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