Graphs Surfaces And Homology

Author : Peter Giblin
Publisher : Cambridge University Press
ISBN 13 : 1139491172
Total Pages : 273 pages
Book Rating : 4.74/5 ( download)

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Download or read book Graphs, Surfaces and Homology written by Peter Giblin and published by Cambridge University Press. This book was released on 2010-08-12 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homology theory is a powerful algebraic tool that is at the centre of current research in topology and its applications. This accessible textbook will appeal to mathematics students interested in the application of algebra to geometrical problems, specifically the study of surfaces (sphere, torus, Mobius band, Klein bottle). In this introduction to simplicial homology - the most easily digested version of homology theory - the author studies interesting geometrical problems, such as the structure of two-dimensional surfaces and the embedding of graphs in surfaces, using the minimum of algebraic machinery and including a version of Lefschetz duality. Assuming very little mathematical knowledge, the book provides a complete account of the algebra needed (abelian groups and presentations), and the development of the material is always carefully explained with proofs given in full detail. Numerous examples and exercises are also included, making this an ideal text for undergraduate courses or for self-study.

Author : P. Giblin
Publisher : Springer Science & Business Media
ISBN 13 : 9400959532
Total Pages : 339 pages
Book Rating : 4.38/5 ( download)

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Download or read book Graphs, Surfaces and Homology written by P. Giblin and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: viii homology groups. A weaker result, sufficient nevertheless for our purposes, is proved in Chapter 5, where the reader will also find some discussion of the need for a more powerful in variance theorem and a summary of the proof of such a theorem. Secondly the emphasis in this book is on low-dimensional examples the graphs and surfaces of the title since it is there that geometrical intuition has its roots. The goal of the book is the investigation in Chapter 9 of the properties of graphs in surfaces; some of the problems studied there are mentioned briefly in the Introduction, which contains an in formal survey of the material of the book. Many of the results of Chapter 9 do indeed generalize to higher dimensions (and the general machinery of simplicial homology theory is avai1able from earlier chapters) but I have confined myself to one example, namely the theorem that non-orientable closed surfaces do not embed in three-dimensional space. One of the principal results of Chapter 9, a version of Lefschetz duality, certainly generalizes, but for an effective presentation such a gener- ization needs cohomology theory. Apart from a brief mention in connexion with Kirchhoff's laws for an electrical network I do not use any cohomology here. Thirdly there are a number of digressions, whose purpose is rather to illuminate the central argument from a slight dis tance, than to contribute materially to its exposition.

Author : Peter J. Giblin
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.78/5 ( download)

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Download or read book Graphs, surfaces and homology : an introduction to algebraic topology written by Peter J. Giblin and published by . This book was released on 1981 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : P. Giblin
Publisher :
ISBN 13 : 9789400959545
Total Pages : 348 pages
Book Rating : 4.40/5 ( download)

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Download or read book Graphs, Surfaces and Homology written by P. Giblin and published by . This book was released on 2014-01-15 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : P. J. Giblin
Publisher :
ISBN 13 : 9780412214400
Total Pages : 329 pages
Book Rating : 4.07/5 ( download)

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Download or read book Graphs, Surfaces and Homology written by P. J. Giblin and published by . This book was released on 1977-01-01 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : P. J. Giblin
Publisher :
ISBN 13 : 9780511902192
Total Pages : 273 pages
Book Rating : 4.90/5 ( download)

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Download or read book Graphs, Surfaces and Homology written by P. J. Giblin and published by . This book was released on 2014-05-14 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: An elementary introduction to homology theory suitable for undergraduate courses or for self-study.

Author : L.Christine Kinsey
Publisher : Springer Science & Business Media
ISBN 13 : 1461208998
Total Pages : 290 pages
Book Rating : 4.90/5 ( download)

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Download or read book Topology of Surfaces written by L.Christine Kinsey and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: " . . . that famous pedagogical method whereby one begins with the general and proceeds to the particular only after the student is too confused to understand even that anymore. " Michael Spivak This text was written as an antidote to topology courses such as Spivak It is meant to provide the student with an experience in geomet describes. ric topology. Traditionally, the only topology an undergraduate might see is point-set topology at a fairly abstract level. The next course the average stu dent would take would be a graduate course in algebraic topology, and such courses are commonly very homological in nature, providing quick access to current research, but not developing any intuition or geometric sense. I have tried in this text to provide the undergraduate with a pragmatic introduction to the field, including a sampling from point-set, geometric, and algebraic topology, and trying not to include anything that the student cannot immediately experience. The exercises are to be considered as an in tegral part of the text and, ideally, should be addressed when they are met, rather than at the end of a block of material. Many of them are quite easy and are intended to give the student practice working with the definitions and digesting the current topic before proceeding. The appendix provides a brief survey of the group theory needed.

Author : Sergei K. Lando
Publisher : Springer Science & Business Media
ISBN 13 : 3540383611
Total Pages : 463 pages
Book Rating : 4.11/5 ( download)

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Download or read book Graphs on Surfaces and Their Applications written by Sergei K. Lando and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs (Grothendieck's theory of "dessins d'enfants"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous figures, examples (including computer calculations) and exercises, and should appeal to both graduate students and researchers.

Author : Herbert Edelsbrunner
Publisher : American Mathematical Society
ISBN 13 : 1470467690
Total Pages : 241 pages
Book Rating : 4.92/5 ( download)

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Download or read book Computational Topology written by Herbert Edelsbrunner and published by American Mathematical Society. This book was released on 2022-01-31 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering. The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.

Author : A.T. White
Publisher : Elsevier
ISBN 13 : 9780080871196
Total Pages : 313 pages
Book Rating : 4.94/5 ( download)

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Download or read book Graphs, Groups and Surfaces written by A.T. White and published by Elsevier. This book was released on 1985-01-01 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared. The original nine chapters of this classic work have therefore been revised and updated. Six new chapters have been added, dealing with: voltage graphs, non-orientable imbeddings, block designs associated with graph imbeddings, hypergraph imbeddings, map automorphism groups and change ringing. Thirty-two new problems have been added to this new edition, so that there are now 181 in all; 22 of these have been designated as ``difficult'' and 9 as ``unsolved''. Three of the four unsolved problems from the first edition have been solved in the ten years between editions; they are now marked as ``difficult''.