Overview

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.

Full Product Details

Author:   Noboru Ito (Waseda Institute for Advanced Study, Shinjuku-ku, Japan)
Publisher:   Taylor & Francis Inc
Imprint:   Chapman & Hall/CRC
Dimensions:   Width: 15.60cm , Height: 1.50cm , Length: 23.40cm
Weight:   0.430kg
ISBN:  

9781498736756

ISBN 10:   1498736750
Pages:   200
Publication Date:   01 December 2016
Audience:   College/higher education ,  College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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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.

Reviews

Overall, this book's clear exposition makes it equally approachable to experts working in knot theory and graduate students who are just learning about the subject. It provides a comprehensive guide to current research on knot projections and different notions of equivalence along with many interesting exercises and open questions for exploration. - Allison Henrich, Mathematical Reviews, July 2017

Author Information

Noboru Ito is currently a project researcher at the University of Tokyo, Japan. He was previously an assistant professor and associate professor of Mathematics at the Waseda Institute for Advanced Study, in Tokyo, Japan.

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