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Topology and Geometry

1993-06-24 Mathematics
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Release : 1993-06-24
Genre : Mathematics
Kind : eBook
Book Rating : 263/5 ( reviews)

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Book Synopsis Topology and Geometry by : Glen E. Bredon

Download or read book Topology and Geometry written by Glen E. Bredon. This book was released on 1993-06-24. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS

Geometry and Topology

2005-11-10 Mathematics
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Release : 2005-11-10
Genre : Mathematics
Kind : eBook
Book Rating : 893/5 ( reviews)

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Book Synopsis Geometry and Topology by : Miles Reid

Download or read book Geometry and Topology written by Miles Reid. This book was released on 2005-11-10. Available in PDF, EPUB and Kindle. Book excerpt: Geometry aims to describe the world around us. It is central to many branches of mathematics and physics, and offers a whole range of views on the universe. This is an introduction to the ideas of geometry and includes generous helpings of simple explanations and examples. The book is based on many years teaching experience so is thoroughly class-tested, and as prerequisites are minimal, it is suited to newcomers to the subject. There are plenty of illustrations; chapters end with a collection of exercises, and solutions are available for teachers.

Introduction to Topology and Geometry

2014-08-21 Mathematics
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Release : 2014-08-21
Genre : Mathematics
Kind : eBook
Book Rating : 148/5 ( reviews)

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Book Synopsis Introduction to Topology and Geometry by : Saul Stahl

Download or read book Introduction to Topology and Geometry written by Saul Stahl. This book was released on 2014-08-21. Available in PDF, EPUB and Kindle. Book excerpt: An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition “. . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained.” —CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparalleled range of topics. Illustrating modern mathematical topics, Introduction to Topology and Geometry, Second Edition discusses introductory topology, algebraic topology, knot theory, the geometry of surfaces, Riemann geometries, fundamental groups, and differential geometry, which opens the doors to a wealth of applications. With its logical, yet flexible, organization, the Second Edition: • Explores historical notes interspersed throughout the exposition to provide readers with a feel for how the mathematical disciplines and theorems came into being • Provides exercises ranging from routine to challenging, allowing readers at varying levels of study to master the concepts and methods • Bridges seemingly disparate topics by creating thoughtful and logical connections • Contains coverage on the elements of polytope theory, which acquaints readers with an exposition of modern theory Introduction to Topology and Geometry, Second Edition is an excellent introductory text for topology and geometry courses at the upper-undergraduate level. In addition, the book serves as an ideal reference for professionals interested in gaining a deeper understanding of the topic.

Topology and Geometry for Physicists

2013-08-16 Mathematics
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Release : 2013-08-16
Genre : Mathematics
Kind : eBook
Book Rating : 362/5 ( reviews)

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Book Synopsis Topology and Geometry for Physicists by : Charles Nash

Download or read book Topology and Geometry for Physicists written by Charles Nash. This book was released on 2013-08-16. Available in PDF, EPUB and Kindle. Book excerpt: Written by physicists for physics students, this text assumes no detailed background in topology or geometry. Topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory. 1983 edition.

Geometric Topology in Dimensions 2 and 3

2013-06-29 Mathematics
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Release : 2013-06-29
Genre : Mathematics
Kind : eBook
Book Rating : 063/5 ( reviews)

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Book Synopsis Geometric Topology in Dimensions 2 and 3 by : E.E. Moise

Download or read book Geometric Topology in Dimensions 2 and 3 written by E.E. Moise. This book was released on 2013-06-29. Available in PDF, EPUB and Kindle. Book excerpt: Geometric topology may roughly be described as the branch of the topology of manifolds which deals with questions of the existence of homeomorphisms. Only in fairly recent years has this sort of topology achieved a sufficiently high development to be given a name, but its beginnings are easy to identify. The first classic result was the SchOnflies theorem (1910), which asserts that every 1-sphere in the plane is the boundary of a 2-cell. In the next few decades, the most notable affirmative results were the "Schonflies theorem" for polyhedral 2-spheres in space, proved by J. W. Alexander [Ad, and the triangulation theorem for 2-manifolds, proved by T. Rad6 [Rd. But the most striking results of the 1920s were negative. In 1921 Louis Antoine [A ] published an extraordinary paper in which he 4 showed that a variety of plausible conjectures in the topology of 3-space were false. Thus, a (topological) Cantor set in 3-space need not have a simply connected complement; therefore a Cantor set can be imbedded in 3-space in at least two essentially different ways; a topological 2-sphere in 3-space need not be the boundary of a 3-cell; given two disjoint 2-spheres in 3-space, there is not necessarily any third 2-sphere which separates them from one another in 3-space; and so on and on. The well-known "horned sphere" of Alexander [A ] appeared soon thereafter.

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