Knotted Surfaces and Their Diagrams

Knotted Surfaces and Their Diagrams

AngličtinaPevná vazba
Saito Masahico
American Mathematical Society
EAN: 9780821805930
Titul je vyprodán u vydavatele, prodej skončil
Neznámé datum dodání
3 125 Kč
Běžná cena: 3 472 Kč
Sleva 10 %
Chcete tento titul ještě dnes?
knihkupectví Megabooks Praha Korunní
není dostupné
Librairie Francophone Praha Štěpánská
není dostupné
knihkupectví Megabooks Ostrava
není dostupné
knihkupectví Megabooks Olomouc
není dostupné
knihkupectví Megabooks Plzeň
není dostupné
knihkupectví Megabooks Brno
není dostupné
knihkupectví Megabooks Hradec Králové
není dostupné
knihkupectví Megabooks České Budějovice
není dostupné
knihkupectví Megabooks Liberec
není dostupné

Dostupné formáty

Podrobné informace

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.
EAN 9780821805930
ISBN 0821805932
Typ produktu Pevná vazba
Vydavatel American Mathematical Society
Datum vydání 30. prosince 1997
Stránky 258
Jazyk English
Země United States
Autoři Saito Masahico
Ilustrace Illustrations
Série Mathematical Surveys and Monographs
Informace o výrobci
Kontaktní informace výrobce nejsou momentálně dostupné online, na nápravě intenzivně pracujeme. Pokud informaci potřebujete, napište nám na info@megabooks.cz, rádi Vám ji poskytneme.