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Author : Armand Borel
Publisher : Springer
ISBN 13 : 3540349758
Total Pages : 100 pages
Book Rating : 4.5/5 (43 download)
Download or read book Topics in the Homology Theory of Fibre Bundles written by Armand Borel and published by Springer. This book was released on 2006-11-14 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Armand Borel
Publisher :
ISBN 13 :
Total Pages : 232 pages
Book Rating : 4.:/5 (276 download)
Download or read book Selected Topics in the Homology Theory of Fibre Bundles written by Armand Borel and published by . This book was released on 1954 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Armand Borel
Publisher :
ISBN 13 :
Total Pages : 95 pages
Book Rating : 4.:/5 (12 download)
Download or read book Topics in the Homology Theory of Fibre Bundles written by Armand Borel and published by . This book was released on 1967 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Armand Borel
Publisher :
ISBN 13 :
Total Pages : 95 pages
Book Rating : 4.:/5 (87 download)
Download or read book Topics in the Homology Theory of Fibre Bundles written by Armand Borel and published by . This book was released on 1967 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Norman Earl Steenrod
Publisher :
ISBN 13 :
Total Pages : 250 pages
Book Rating : 4.3/5 (91 download)
Download or read book The Topology of Fibre Bundles written by Norman Earl Steenrod and published by . This book was released on 1951 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fibre bundles, now an integral part of differential geometry, are also of great importance in modern physics--such as in gauge theory. This book, a succinct introduction to the subject by renown mathematician Norman Steenrod, was the first to present the subject systematically. It begins with a general introduction to bundles, including such topics as differentiable manifolds and covering spaces. The author then provides brief surveys of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles. The result is a classic and timeless work of great utility that will appeal to serious mathematicians and theoretical physicists alike.
Author : Norman Steenrod
Publisher : Princeton University Press
ISBN 13 : 0691005486
Total Pages : 240 pages
Book Rating : 4.6/5 (91 download)
Download or read book The Topology of Fibre Bundles written by Norman Steenrod and published by Princeton University Press. This book was released on 1999-04-25 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fibre bundles, now an integral part of differential geometry, are also of great importance in modern physics--such as in gauge theory. This book, a succinct introduction to the subject by renown mathematician Norman Steenrod, was the first to present the subject systematically. It begins with a general introduction to bundles, including such topics as differentiable manifolds and covering spaces. The author then provides brief surveys of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles. The result is a classic and timeless work of great utility that will appeal to serious mathematicians and theoretical physicists alike.
Author : Dale Husemöller
Publisher : Springer Science & Business Media
ISBN 13 :
Total Pages : 356 pages
Book Rating : 4.3/5 (91 download)
Download or read book Fibre Bundles written by Dale Husemöller and published by Springer Science & Business Media. This book was released on 1975 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Armand Borel
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (878 download)
Download or read book Topics in the Homolohy Theory of Fibre Bundles written by Armand Borel and published by . This book was released on 1967 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mahima Ranjan Adhikari
Publisher : Springer Nature
ISBN 13 : 9811665508
Total Pages : 488 pages
Book Rating : 4.8/5 (116 download)
Download or read book Basic Topology 3 written by Mahima Ranjan Adhikari and published by Springer Nature. This book was released on 2023-03-15 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third of the three-volume book is targeted as a basic course in algebraic topology and topology for fiber bundles for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, and algebra. Topics covered in this volume include homotopy theory, homology and cohomology theories, homotopy theory of fiber bundles, Euler characteristic, and the Betti number. It also includes certain classic problems such as the Jordan curve theorem along with the discussions on higher homotopy groups and establishes links between homotopy and homology theories, axiomatic approach to homology and cohomology as inaugurated by Eilenberg and Steenrod. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power and active learning of the subject, all the while covering a wide range of theory and applications in a balanced unified way.
Author : Junpei Sekino
Publisher :
ISBN 13 :
Total Pages : 276 pages
Book Rating : 4.:/5 (98 download)
Download or read book Homology Theory of Submersions written by Junpei Sekino and published by . This book was released on 1974 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation we construct a homology theory on the category of submersions which generalizes the homology of the base space with coefficients in the homology of the fiber as given by the E2-terms of the Serre spectral sequence of a fiber bundle. The main motivation for this new homology theory is the fact that it permits a generalization of the Serre spectral sequence to arbitrary submersions. The homology theory in question is first defined on a category of combinatorial objects called simplicial bundles which at once generalize the notion of fiber bundles (over polyhedra) and simplicial complexes. We next enlarge the category of submersions to include all direct limits of simplicial bundles and extend the homology functor by a category-theoretic construction. The resultant theory is shown to satisfy axioms of Eilenberg-Steenrod type, and we prove a uniqueness theorem.
Author : Norman E. Steenrod
Publisher :
ISBN 13 :
Total Pages : 227 pages
Book Rating : 4.:/5 (934 download)
Download or read book The Topology of Fibre Bundles written by Norman E. Steenrod and published by . This book was released on 1970 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Dai Tamaki
Publisher :
ISBN 13 : 9789811238093
Total Pages : 337 pages
Book Rating : 4.2/5 (38 download)
Download or read book Fiber Bundles And Homotopy written by Dai Tamaki and published by . This book was released on 2021 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is an introduction to fiber bundles and fibrations. But the ultimate goal is to make the reader feel comfortable with basic ideas in homotopy theory. The author found that the classification of principal fiber bundles is an ideal motivation for this purpose. The notion of homotopy appears naturally in the classification. Basic tools in homotopy theory such as homotopy groups and their long exact sequence need to be introduced. Furthermore, the notion of fibrations, which is one of three important classes of maps in homotopy theory, can be obtained by extracting the most essential properties of fiber bundles. The book begins with elementary examples and then gradually introduces abstract definitions when necessary. The reader is assumed to be familiar with point-set topology, but it is the only requirement for this book"--
Author : J.L. Koszul
Publisher : Springer
ISBN 13 :
Total Pages : 148 pages
Book Rating : 4.E/5 ( download)
Download or read book Lectures on Fibre Bundles and Differential Geometry written by J.L. Koszul and published by Springer. This book was released on 1987 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topic of these notes is the theory of connections. There are two basic notions in the theory: the notion of covariant derivation which concerns differentiable sections of vector bundles, and th~ notion of connection forms on principal bundles. These two notions Hre by no means independent of each other. While any law of covariant derivation in a vector bundle can be defined by a connection forn in the princip21 bundle of framee, an independent treatment of covariant doriv~tions is desirable in view of many applications wh~re the principal bundle remains in the background. In the first chapter, we start with an algebraic formulation of covariant derivations. The rela"i:,ed notions of curvature, differen tials and torsion are discussed without reference to manifolds. Chapters II, III and IV are devoted to a study of connection forms on principal bundles. Chapter V deals essentially with the relations bet ween covariant derivations and co:mcction forms. Some special features of the theory of connections in almost complex and holomorphic bundles, which include the recent results of Atiyah ~2-1 form the subject matter of the final chapter. We have not dealt with any topic related to the theory of characteristic forms or that of "Cartan connections" in the sense of 11 Ehresmann, but a few referencos in these directions are given in the bibliography.
Author : Tammo tom Dieck
Publisher : European Mathematical Society
ISBN 13 : 9783037190487
Total Pages : 584 pages
Book Rating : 4.1/5 (94 download)
Download or read book Algebraic Topology written by Tammo tom Dieck and published by European Mathematical Society. This book was released on 2008 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written as a textbook on algebraic topology. The first part covers the material for two introductory courses about homotopy and homology. The second part presents more advanced applications and concepts (duality, characteristic classes, homotopy groups of spheres, bordism). The author recommends starting an introductory course with homotopy theory. For this purpose, classical results are presented with new elementary proofs. Alternatively, one could start more traditionally with singular and axiomatic homology. Additional chapters are devoted to the geometry of manifolds, cell complexes and fibre bundles. A special feature is the rich supply of nearly 500 exercises and problems. Several sections include topics which have not appeared before in textbooks as well as simplified proofs for some important results. Prerequisites are standard point set topology (as recalled in the first chapter), elementary algebraic notions (modules, tensor product), and some terminology from category theory. The aim of the book is to introduce advanced undergraduate and graduate (master's) students to basic tools, concepts and results of algebraic topology. Sufficient background material from geometry and algebra is included.
Author : John Frank Adams
Publisher : Cambridge University Press
ISBN 13 : 9780521410656
Total Pages : 552 pages
Book Rating : 4.4/5 (16 download)
Download or read book The Selected Works of J. Frank Adams: Volume 2 written by John Frank Adams and published by Cambridge University Press. This book was released on 1992-10-07 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: The selected works of one the greatest names in algebraic topology.
Author : Stephen Smale
Publisher : World Scientific
ISBN 13 : 9789810249915
Total Pages : 532 pages
Book Rating : 4.2/5 (499 download)
Download or read book The Collected Papers of Stephen Smale written by Stephen Smale and published by World Scientific. This book was released on 2000 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book contains the collected papers of Stephen Smale. These are divided into eight groups: topology; calculus of variations; dynamics; mechanics; economics; biology, electric circuits and mathematical programming; theory of computation; miscellaneous. In addition, each group contains one or two articles by world leaders on its subject which comment on the influence of Smale's work, and another article by Smale with his own retrospective views.
Author : Paul Emery Thomas
Publisher :
ISBN 13 :
Total Pages : 140 pages
Book Rating : 4.3/5 (91 download)
Download or read book On the Cohomology of the Real Grassman Manifolds and the Characteristics of Classes of N-plane Bundles written by Paul Emery Thomas and published by . This book was released on 1958 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
