Topology Of Surfaces
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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.
Geometry And Topology Of Surfaces
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Author : Sebastian Baader
language : en
Publisher:
Release Date : 2021
Geometry And Topology Of Surfaces written by Sebastian Baader and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
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.
Topology Of Surfaces
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Author : André Gramain
language : en
Publisher:
Release Date : 1984
Topology Of Surfaces written by André Gramain and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 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
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.
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.
Topological Differential And Conformal Geometry Of Surfaces
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Author : Norbert A'Campo
language : en
Publisher: Springer Nature
Release Date : 2021-10-27
Topological Differential And Conformal Geometry Of Surfaces written by Norbert A'Campo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-27 with Mathematics categories.
This book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces. It first covers the prerequisites, including the basics of differential forms, the Poincaré Lemma, the Morse Lemma, the classification of compact connected oriented surfaces, Stokes’ Theorem, fixed point theorems and rigidity theorems. There is also a novel presentation of planar hyperbolic geometry. Moving on to more advanced concepts, it covers topics such as Riemannian metrics, the isometric torsion-free connection on vector fields, the Ansatz of Koszul, the Gauss–Bonnet Theorem, and integrability. These concepts are then used for the study of Riemann surfaces. One of the focal points is the Uniformization Theorem for compact surfaces, an elementary proof of which is given via a property of the energy functional. Among numerous other results, there is also a proof of Chow’s Theorem on compact holomorphic submanifolds in complex projective spaces. Based on lecture courses given by the author, the book will be accessible to undergraduates and graduates interested in the analytic theory of Riemann surfaces.
Topology Of Surfaces Knots And Manifolds
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Author : Johanna Adison
language : en
Publisher:
Release Date : 2016-10-01
Topology Of Surfaces Knots And Manifolds written by Johanna Adison and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-01 with categories.
Since the early part of the 20th century both topology and analysis have fed off each other and this has resulted in some very beautiful theorems that lie at the interface between these two disciplines. Perhaps the best known example of these is Brouwer's fixed point theorem (later generalised by J. Schauder to more general spaces) which has had countless applications in applied mathematics, economics and analysis itself. Topology is the study of those properties of objects that are preserved under careful deformation. Topology is the area of mathematics which investigates continuity and related concepts. Important fundamental notions soon to come are for example open and closed sets, continuity, and homeomorphism. Originally coming from questions in analysis and differential geometry, by now topology permeates mostly every field of math including algebra, combinatorics, logic, and plays a fundamental role in algebraic/arithmetic geometry as we know it today. s Topology of Surfaces, Knots, and Manifolds offers an intuition-based and applied approach to the basic ideas and problems involving manifolds, particularly one- and two-dimensional manifolds. A comprehensive, self-contained treatment presenting general results of the theory.
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.