Graphs Surfaces And Homology
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Graphs Surfaces And Homology
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Author : P. Giblin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Graphs Surfaces And Homology written by P. Giblin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Social Science categories.
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.
Graphs Surfaces And Homology
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Author : Peter Giblin
language : en
Publisher: Cambridge University Press
Release Date : 2010-08-12
Graphs Surfaces And Homology written by Peter Giblin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-12 with Mathematics categories.
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.
Graphs Surfaces And Homology An Introduction To Algebraic Topology
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Author : Peter J. Giblin
language : en
Publisher:
Release Date : 1981
Graphs Surfaces And Homology An Introduction To Algebraic Topology written by Peter J. Giblin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Graphs Surfaces And Homology
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Author : P. J. Giblin
language : en
Publisher:
Release Date : 2010
Graphs Surfaces And Homology written by P. J. Giblin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Algebraic topology categories.
An elementary introduction to homology theory suitable for undergraduate courses or for self-study.
Graphs Surfaces And Homology
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Author : P. J. Giblin
language : en
Publisher:
Release Date : 1977-01-01
Graphs Surfaces And Homology written by P. J. Giblin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-01-01 with Abelian groups categories.
Graphs Surfaces And Homology
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Author : P. Giblin
language : en
Publisher:
Release Date : 2014-01-15
Graphs Surfaces And Homology written by P. Giblin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Graphs Surfaces And Homology By Peter Giblin
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Author : Peter Giblin
language : en
Publisher:
Release Date : 2010
Graphs Surfaces And Homology By Peter Giblin written by Peter Giblin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Algebraic topology categories.
Handbook Of Discrete And Computational Geometry
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Author : Csaba D. Toth
language : en
Publisher: CRC Press
Release Date : 2017-11-22
Handbook Of Discrete And Computational Geometry written by Csaba D. Toth and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Computers categories.
The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.
Topology Of Surfaces
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Author : L.Christine Kinsey
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-09-26
Topology Of Surfaces written by L.Christine Kinsey and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-09-26 with Mathematics categories.
" . . . 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.
Algorithms Esa 2010
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Author : Mark de Berg
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-30
Algorithms Esa 2010 written by Mark de Berg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-30 with Computers categories.
This book constitutes the proceedings of the 18th Annual European Symposium on Algorithms, held in Liverpool, UK in September 2010.