Surface Topology
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Surface Topology
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Author : P. A. Firby
language : en
Publisher:
Release Date : 1982
Surface Topology written by P. A. Firby and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
Surface Topology
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Author : P A Firby
language : en
Publisher: Elsevier
Release Date : 2001-06-01
Surface Topology written by P A Firby and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-01 with Mathematics categories.
This updated and revised edition of a widely acclaimed and successful text for undergraduates examines topology of recent compact surfaces through the development of simple ideas in plane geometry. Containing over 171 diagrams, the approach allows for a straightforward treatment of its subject area. It is particularly attractive for its wealth of applications and variety of interactions with branches of mathematics, linked with surface topology, graph theory, group theory, vector field theory, and plane Euclidean and non-Euclidean geometry. Examines topology of recent compact surfaces through the development of simple ideas in plane geometry Contains a wealth of applications and a variety of interactions with branches of mathematics, linked with surface topology, graph theory, group theory, vector field theory, and plane Euclidean and non-Euclidean geometry
Topology Of Surfaces
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Author : L.Christine Kinsey
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
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 2012-12-06 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.
How Surfaces Intersect In Space
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Author : J. Scott Carter
language : en
Publisher: World Scientific
Release Date : 1995
How Surfaces Intersect In Space written by J. Scott Carter and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Science categories.
This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader. It will be of value to anyone who wants to understand the subject by way of examples. Undergraduates, beginning graduate students, and non-professionals will profit from reading the book and from just looking at the pictures.
Topological Data Structures For Surfaces
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Author : Sanjay Rana
language : en
Publisher: John Wiley & Sons
Release Date : 2005-12-13
Topological Data Structures For Surfaces written by Sanjay Rana and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-13 with Science categories.
In Geography and GIS, surfaces can be analysed and visualised through various data structures, and topological data structures describe surfaces in the form of a relationship between certain surface-specific features. Drawn from many disciplines with a strong applied aspect, this is a research-led, interdisciplinary approach to the creation, analysis and visualisation of surfaces, focussing on topological data structures. Topological Data Structures for Surfaces: an introduction for Geographical Information Science describes the concepts and applications of these data structures. The book focuses on how these data structures can be used to analyse and visualise surface datasets from a range of disciplines such as human geography, computer graphics, metrology, and physical geography. Divided into two Parts, Part I defines the topological surface data structures and explains the various automated methods used for their generation. Part II demonstrates a number of applications of surface networks in diverse fields, ranging from sub-atomic particle collision visualisation to the study of population density patterns. To ensure that the material is accessible, each Part is prefaced by an overview of the techniques and application. Provides GI scientists and geographers with an accessible overview of current surface topology research. Algorithms are presented and explained with practical examples of their usage. Features an accompanying website developed by the Editor - http://geog.le.ac.uk/sanjayrana/surface-networks/ This book is invaluable for researchers and postgraduate students working in departments of GI Science, Geography and Computer Science. It also constitutes key reference material for Masters students working on surface analysis projects as part of a GI Science or Computer Science programme.
Surfaces In 4 Space
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Author : Scott Carter
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Surfaces In 4 Space written by Scott Carter 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 Mathematics categories.
Surfaces in 4-Space, written by leading specialists in the field, discusses knotted surfaces in 4-dimensional space and surveys many of the known results in the area. Results on knotted surface diagrams, constructions of knotted surfaces, classically defined invariants, and new invariants defined via quandle homology theory are presented. The last chapter comprises many recent results, and techniques for computation are presented. New tables of quandles with a few elements and the homology groups thereof are included. This book contains many new illustrations of knotted surface diagrams. The reader of the book will become intimately aware of the subtleties in going from the classical case of knotted circles in 3-space to this higher dimensional case. As a survey, the book is a guide book to the extensive literature on knotted surfaces and will become a useful reference for graduate students and researchers in mathematics and physics.
Topology Of Surfaces Knots And Manifolds
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Author : Stephan C. Carlson
language : en
Publisher: John Wiley & Sons
Release Date : 2001-01-10
Topology Of Surfaces Knots And Manifolds written by Stephan C. Carlson and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-10 with Mathematics categories.
This textbook contains ideas and problems involving curves, surfaces, and knots, which make up the core of topology. Carlson (mathematics, Rose-Hulman Institute of Technology) introduces some basic ideas and problems concerning manifolds, especially one- and two- dimensional manifolds. A sampling of topics includes classification of compact surfaces, putting more structure on the surfaces, graphs and topology, and knot theory. It is assumed that the reader has a background in calculus. Annotation copyrighted by Book News Inc., Portland, OR.
Elements Of The Geometry And Topology Of Minimal Surfaces In Three Dimensional Space
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Author : A. T. Fomenko
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Elements Of The Geometry And Topology Of Minimal Surfaces In Three Dimensional Space written by A. T. Fomenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
This book grew out of lectures presented to students of mathematics, physics, and mechanics by A. T. Fomenko at Moscow University, under the auspices of the Moscow Mathematical Society. The book describes modern and visual aspects of the theory of minimal, two-dimensional surfaces in three-dimensional space. The main topics covered are: topological properties of minimal surfaces, stable and unstable minimal films, classical examples, the Morse-Smale index of minimal two-surfaces in Euclidean space, and minimal films in Lobachevskian space. Requiring only a standard first-year calculus and elementary notions of geometry, this book brings the reader rapidly into this fascinating branch of modern geometry.
Geometry And Topology Of Manifolds Surfaces And Beyond
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Author : Vicente Muñoz
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-10-21
Geometry And Topology Of Manifolds Surfaces And Beyond written by Vicente Muñoz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-21 with Education categories.
This book represents a novel approach to differential topology. Its main focus is to give a comprehensive introduction to the classification of manifolds, with special attention paid to the case of surfaces, for which the book provides a complete classification from many points of view: topological, smooth, constant curvature, complex, and conformal. Each chapter briefly revisits basic results usually known to graduate students from an alternative perspective, focusing on surfaces. We provide full proofs of some remarkable results that sometimes are missed in basic courses (e.g., the construction of triangulations on surfaces, the classification of surfaces, the Gauss-Bonnet theorem, the degree-genus formula for complex plane curves, the existence of constant curvature metrics on conformal surfaces), and we give hints to questions about higher dimensional manifolds. Many examples and remarks are scattered through the book. Each chapter ends with an exhaustive collection of problems and a list of topics for further study. The book is primarily addressed to graduate students who did take standard introductory courses on algebraic topology, differential and Riemannian geometry, or algebraic geometry, but have not seen their deep interconnections, which permeate a modern approach to geometry and topology of manifolds.
A Guide To The Classification Theorem For Compact Surfaces
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Author : Jean Gallier
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-02-05
A Guide To The Classification Theorem For Compact Surfaces written by Jean Gallier 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 2013-02-05 with Mathematics categories.
This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy and formal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example. Ideal for students whose mastery of algebraic topology may be a work-in-progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincaré characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learning where it is required, without interrupting the carefully planned structure of the core exposition. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuine confidence in its use and in so doing encourage readers to move on to a deeper exploration of the versatile and valuable techniques available in algebraic topology.