Knot projections
by Ito, Noboru
Knot Projections offers a comprehensive overview of the latest methods in the study of this branch of topology, based on current research inspired by Arnolds theory of plane curves, Viros quantization of the Arnold invariant, and Vassilievs 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 subj…
Read More ↓Title Statements
- Full title :Knot projections / Noboru Ito, the University of Tokyo, Meguro-ku, Tokyo, Japan.
Summary
Knot Projections offers a comprehensive overview of the latest methods in the study of this branch of topology, based on current research inspired by Arnolds theory of plane curves, Viros quantization of the Arnold invariant, and Vassilievs 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.
Read More ↓Edition Statements
- Publication Date:©2016
Publication Statements
- Publisher(s):Chapman and Hall/CRC, CRC Press LLC
- Place of Publication:Boca Raton, FL
- Language:eng
- Publication Date:©2016
The Physical Object
- Description:1 online resource (xix, 200 pages) : : illustrations
Edition Identifiers
- ISBN:9781498736770, 1498736777, 1315369575, 9781315369570
- DOI:10.1201/9781315369570
- oclc:ocn988084541
- LC Classification:QA612.2
- Dewey Decimal:514/.2242
Table of Contents
Knots, knot diagrams, and knot projections -- Mathematical background, 1920s -- Topological invariant of know projections, 1930s -- Classification of knot projections under RI and RII, 1990s -- Classification by RI and strong or weak RIII, 1996-2015 -- Techniques for counting sub-chord diagrams, 2015-future -- Hagge-Yazinski theorem, necessity of RIII -- Further result of strong (1, 3) homotopy -- Half-twisted splice operations, reductivities, unavoidable sets, triple chords, and strong (1, 2) homotopy -- Weak (1, 2, 3) homotopy -- Viro's quantization of Arnold invariant.
Read More ↓Subjects
Writers
More from this Series
No reviews yet. Be the first to rate this work.
Related Works
more →
Files & Downloads
-
Knot projections -- (.pdf)
PDF · 2.5 MB · updated
Rate & Review