How Surfaces Intersect In Space

An Introduction To Topology (2nd Edition)

J Scott Carter (Univ Of South Alabama, Usa)

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Paperback

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English

World Scientific Publishing Co Pte Ltd
01 January 2024

Geometry; Topology

Series: Series on Knots & Everything

This is a book of pictures that illustrate standard examples in low dimensional topology. The text starts at the most basic level (the intersection of coordinate planes) and gives hands-on constructions of the most beautiful 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 carefully explains the importance of the examples and the techniques without being bogged down in a morass of technicalities. The book is a guide book to a wide variety of topics. It will be of value 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. Finally, the book should be interesting to other scientists and mathematicians who want to learn some examples of topological spaces.

By: J Scott Carter (Univ Of South Alabama Usa)
Imprint: World Scientific Publishing Co Pte Ltd
Country of Publication: Singapore
Edition: 2nd Revised edition
Volume: 2
Dimensions: Height: 220mm, Width: 151mm, Spine: 19mm
Weight: 476g
ISBN: 9789810220662
ISBN 10: 9810220669
Series: Series on Knots & Everything
Pages: 338
Publication Date: 01 January 2024
Audience: College/higher education , Professional and scholarly , Professional & Vocational , A / AS level , Further / Higher Education
Format: Paperback
Publisher's Status: Unspecified

Classification of orientable surfaces, and the meaning of space; examples of non-orientable surfaces including models of the projective plane and the Klein bottle; how curves fit on surfaces and gives a general discussion of knotted strings in space; some examples of other 3-dimensional spaces - the 3-dimensional sphere, lens spaces, the quaternionic projective space; movie techniques of studying surfaces in 4-dimensions - how to move among the standard examples of Klein bottles, ""movie move"" decomposition of turning the 2-sphere inside out; higher dimensional spaces.