CONSTRUCTION OF INVARIANTS OF CURVES AND FRONTS USING WORD THEORY-Reference-Cited by-同舟云学术

CONSTRUCTION OF INVARIANTS OF CURVES AND FRONTS USING WORD THEORY

Published:2010-09 Issue:09 Volume:19 Page:1205-1245
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

ITO NOBORU¹

Affiliation:

1. Department of Pure and Applied Mathematics, Graduate School of Fundamental Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjyuku-ku, Tokyo 169-8555, Japan

Abstract

We construct an infinite sequence of invariants for surface curves by using the word theory introduced by Turaev. We modify these invariants to various classes of curves: plane closed curves, long curves and fronts. For a plane closed curve, for example, these modified invariants contain Arnold's basic invariants. We also discuss how curves are classified by these modified invariants.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216510008406

Reference17 articles.

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2. Lectures on topology of words

3. V. A. Vassiliev, Theory of Singularities and Its Applications, Advances in Soviet Mathematics 1 (American Mathematical Society, Providence, RI, 1990) pp. 23–69.

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