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How Surfaces Intersect In Space: An Introduction To Topology (2Nd Edition): 2 (SERIES ON KNOTS AND EVERYTHING) - Tapa blanda

Carter, Univ South Alabama J Scott

 
9789810220822: How Surfaces Intersect In Space: An Introduction To Topology (2Nd Edition): 2 (SERIES ON KNOTS AND EVERYTHING)
Tapa blanda
ISBN 10: 9810220820 ISBN 13: 9789810220822
Editorial: Wspc, 1995

Sinopsis

This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader. The first chapter discusses the meaning of surface and space and gives the classification of orientable surfaces. In the second chapter we are introduced to the Möbius band and surfaces that can be constructed from this non-orientable piece of fabric. In chapter 3, we see how curves can fit in surfaces and how surfaces can fit into spaces with these curves on their boundary. Basic applications to knot theory are discussed and four-dimensional space is introduced.In Chapter 4 we learn about some 3-dimensional spaces and surfaces that sit inside them. These surfaces help us imagine the structures of the larger space.Chapter 5 is completely new! It contains recent results of Cromwell, Izumiya and Marar. One of these results is a formula relating the rank of a surface to the number of triple points. The other major result is a collection of examples of surfaces in 3-space that have one triple point and 6 branch points. These are beautiful generalizations of the Steiner Roman surface.Chapter 6 reviews the movie technique for examining surfaces in 4-dimensional space. Various movies of the Klein bottle are presented, and the Carter-Saito movie move theorem is explained. The author shows us how to turn the 2-sphere inside out by means of these movie moves and this illustration alone is well worth the price of the book!In the last chapter higher dimensional spaces are examined from an elementary point of view.This is a guide book to a wide variety of topics. It will be of value to anyone who wants to understand the subject by way of examples. Undergraduates, beginning graduate students, and non-professionals will profit from reading the book and from just looking at the pictures.

"Sinopsis" puede pertenecer a otra edición de este libro.

Reseña del editor

This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader. The first chapter discusses the meaning of surface and space and gives the classification of orientable surfaces. In the second chapter we are introduced to the Moebius band and surfaces that can be constructed from this non-orientable piece of fabric. In chapter 3, we see how curves can fit in surfaces and how surfaces can fit into spaces with these curves on their boundary. Basic applications to knot theory are discussed and four-dimensional space is introduced.In Chapter 4 we learn about some 3-dimensional spaces and surfaces that sit inside them. These surfaces help us imagine the structures of the larger space.Chapter 5 is completely new! It contains recent results of Cromwell, Izumiya and Marar. One of these results is a formula relating the rank of a surface to the number of triple points. The other major result is a collection of examples of surfaces in 3-space that have one triple point and 6 branch points. These are beautiful generalizations of the Steiner Roman surface.Chapter 6 reviews the movie technique for examining surfaces in 4-dimensional space. Various movies of the Klein bottle are presented, and the Carter-Saito movie move theorem is explained. The author shows us how to turn the 2-sphere inside out by means of these movie moves and this illustration alone is well worth the price of the book!In the last chapter higher dimensional spaces are examined from an elementary point of view.This is a guide book to a wide variety of topics. It will be of value to anyone who wants to understand the subject by way of examples. Undergraduates, beginning graduate students, and non-professionals will profit from reading the book and from just looking at the pictures.

Reseña del editor

This text presents pictures that illustrates standard examples in low dimensional topology. It begins at the most basic level (the intersection of coordinate planes) and gives hands on constructions of examples in topology: the projective plane, Poincare's example of a homology sphere, lens spaces, knotted surfaces, 2-sphere eversions and higher dimensional manifolds. The text explains the importance of the examples and the techniques without being bogged down in technicalities. The book is a guide to a wide variety of topics. It should be of use to undergraduates who want to learn geometric topology and to graduate students who want examples with which they can make computations and who need an elementary description of topological spaces. It should also be interesting to other scientists and mathematicians who want to learn some examples of topological spaces.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Wspc
Año de publicación
1995
Idioma
Inglés
ISBN 10 
9810220820
ISBN 13 
9789810220822
Encuadernación
Tapa blanda
Número de edición
2
Número de páginas
338
Contacto del fabricante
no disponible
Persona responsable
gpsr@libri.de
gpsr@libri.de

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