Knotted Surfaces and Their Diagrams - Mathematical Surveys and Monographs (Hardback)
  • Knotted Surfaces and Their Diagrams - Mathematical Surveys and Monographs (Hardback)
zoom

Knotted Surfaces and Their Diagrams - Mathematical Surveys and Monographs (Hardback)

(author), (author)
£85.50
Hardback 258 Pages / Published: 30/12/1997
  • Publisher out of stock

Currently unavailable to order

This product is currently unavailable.

  • This item has been added to your basket
In this book the authors develop the theory of knotted surfaces in analogy with the classical case of knotted curves in 3-dimensional space. In the first chapter knotted surface diagrams are defined and exemplified; these are generic surfaces in 3-space with crossing information given. The diagrams are further enhanced to give alternative descriptions. A knotted surface can be described as a movie, as a kind of labeled planar graph, or as a sequence of words in which successive words are related by grammatical changes. In the second chapter, the theory of Reidemeister moves is developed in the various contexts.The authors show how to unknot intricate examples using these moves. The third chapter reviews the braid theory of knotted surfaces. Examples of the Alexander isotopy are given, and the braid movie moves are presented. In the fourth chapter, properties of the projections of knotted surfaces are studies. Oriented surfaces in 4-space are shown to have planar projections without cusps and without branch points. Signs of triple points are studied.Applications of triple-point smoothing that include proofs of triple-point formulas and a proof of Whitney's congruence on normal Euler classes are presented. The fifth chapter indicates how to obtain presentations for the fundamental group and the Alexander modules. Key examples are worked in detail. The Seifert algorithm for knotted surfaces is presented and exemplified. The sixth chapter relates knotted surfaces and diagrammatic techniques to 2-categories. Solutions to the Zamolodchikov equations that are diagrammatically obtained are presented. The book contains over 200 illustrations that illuminate the text. Examples are worked out in detail, and readers have the opportunity to learn first-hand a series of remarkable geometric techniques.

Publisher: American Mathematical Society
ISBN: 9780821805930
Number of pages: 258
Weight: 696 g
Dimensions: 267 x 184 mm

You may also be interested in...

Riemann Surfaces
Added to basket
Knots
Added to basket
£16.95
Paperback
Fractals: A Very Short Introduction
Added to basket
The Poincare Conjecture
Added to basket
A Combinatorial Introduction to Topology
Added to basket
Essential Topology
Added to basket
Knot Theory and Its Applications
Added to basket
Introduction to Topology
Added to basket
Algebraic Topology
Added to basket
£30.99
Paperback
Schaums Outline of General Topology
Added to basket
Flatland
Added to basket
£9.99
Paperback

Reviews

Please sign in to write a review

Your review has been submitted successfully.