Topology Of Surfaces
Download Topology Of Surfaces full books in PDF, epub, and Kindle. Read online free Topology Of Surfaces ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads.
Author |
: L.Christine Kinsey |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 304 |
Release |
: 1997-09-26 |
ISBN-10 |
: 0387941029 |
ISBN-13 |
: 9780387941028 |
Rating |
: 4/5 (29 Downloads) |
Synopsis Topology of Surfaces by : L.Christine Kinsey
" . . . 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 |
: Stephan C. Carlson |
Publisher |
: John Wiley & Sons |
Total Pages |
: 178 |
Release |
: 2001-01-10 |
ISBN-10 |
: UOM:39015049686283 |
ISBN-13 |
: |
Rating |
: 4/5 (83 Downloads) |
Synopsis Topology of Surfaces, Knots, and Manifolds by : Stephan C. Carlson
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.
Author |
: Vicente Muñoz |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 420 |
Release |
: 2020-10-21 |
ISBN-10 |
: 9781470461324 |
ISBN-13 |
: 1470461323 |
Rating |
: 4/5 (24 Downloads) |
Synopsis Geometry and Topology of Manifolds: Surfaces and Beyond by : Vicente Muñoz
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.
Author |
: P. A. Firby |
Publisher |
: Halsted Press |
Total Pages |
: 224 |
Release |
: 1982 |
ISBN-10 |
: UOM:39015015610564 |
ISBN-13 |
: |
Rating |
: 4/5 (64 Downloads) |
Synopsis Surface Topology by : P. A. Firby
Author |
: Sebastian Baader |
Publisher |
: |
Total Pages |
: |
Release |
: 2021 |
ISBN-10 |
: 3985470006 |
ISBN-13 |
: 9783985470006 |
Rating |
: 4/5 (06 Downloads) |
Synopsis Geometry and Topology of Surfaces by : Sebastian Baader
Author |
: Richard Evan Schwartz |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 330 |
Release |
: 2011 |
ISBN-10 |
: 9780821853689 |
ISBN-13 |
: 0821853686 |
Rating |
: 4/5 (89 Downloads) |
Synopsis Mostly Surfaces by : Richard Evan Schwartz
The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. --from publisher description.
Author |
: J. Scott Carter |
Publisher |
: World Scientific |
Total Pages |
: 344 |
Release |
: 1995 |
ISBN-10 |
: 9810220669 |
ISBN-13 |
: 9789810220662 |
Rating |
: 4/5 (69 Downloads) |
Synopsis How Surfaces Intersect in Space by : J. Scott Carter
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.
Author |
: Norbert A'Campo |
Publisher |
: Springer Nature |
Total Pages |
: 282 |
Release |
: 2021-10-27 |
ISBN-10 |
: 9783030890322 |
ISBN-13 |
: 3030890325 |
Rating |
: 4/5 (22 Downloads) |
Synopsis Topological, Differential and Conformal Geometry of Surfaces by : Norbert A'Campo
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.
Author |
: Jean Gallier |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 184 |
Release |
: 2013-02-05 |
ISBN-10 |
: 9783642343643 |
ISBN-13 |
: 3642343643 |
Rating |
: 4/5 (43 Downloads) |
Synopsis A Guide to the Classification Theorem for Compact Surfaces by : Jean Gallier
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.
Author |
: Peter Giblin |
Publisher |
: Cambridge University Press |
Total Pages |
: 273 |
Release |
: 2010-08-12 |
ISBN-10 |
: 9781139491174 |
ISBN-13 |
: 1139491172 |
Rating |
: 4/5 (74 Downloads) |
Synopsis Graphs, Surfaces and Homology by : Peter Giblin
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.