Topology Of Surfaces

Author : L.Christine Kinsey
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461208990

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Topology of Surfaces by L.Christine Kinsey Pdf

" . . . 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 : Vicente Muñoz,Ángel González-Prieto,Juan Ángel Rojo
Publisher : American Mathematical Soc.
Page : 408 pages
File Size : 49,7 Mb
Release : 2020-10-21
Category : Education
ISBN : 9781470461324

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Geometry and Topology of Manifolds: Surfaces and Beyond by Vicente Muñoz,Ángel González-Prieto,Juan Ángel Rojo Pdf

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 : Norbert A'Campo
Publisher : Springer Nature
Page : 282 pages
File Size : 53,5 Mb
Release : 2021-10-27
Category : Mathematics
ISBN : 9783030890322

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Topological, Differential and Conformal Geometry of Surfaces by Norbert A'Campo Pdf

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 : P. A. Firby,Cyril F. Gardiner
Publisher : Halsted Press
Page : 224 pages
File Size : 48,5 Mb
Release : 1982
Category : Mathematics
ISBN : UOM:39015015610564

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Surface Topology by P. A. Firby,Cyril F. Gardiner Pdf

Author : Stephan C. Carlson
Publisher : John Wiley & Sons
Page : 178 pages
File Size : 42,8 Mb
Release : 2001-01-10
Category : Mathematics
ISBN : UOM:39015049686283

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Topology of Surfaces, Knots, and Manifolds by Stephan C. Carlson Pdf

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 : Sebastian Baader
Publisher : Unknown
Page : 128 pages
File Size : 49,9 Mb
Release : 2021
Category : Electronic
ISBN : 3985470006

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Geometry and Topology of Surfaces by Sebastian Baader Pdf

Author : Richard Evan Schwartz
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 45,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821853689

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Mostly Surfaces by Richard Evan Schwartz Pdf

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 : Jean Gallier,Dianna Xu
Publisher : Springer Science & Business Media
Page : 184 pages
File Size : 46,6 Mb
Release : 2013-02-05
Category : Mathematics
ISBN : 9783642343643

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A Guide to the Classification Theorem for Compact Surfaces by Jean Gallier,Dianna Xu Pdf

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 : J. Scott Carter
Publisher : World Scientific
Page : 344 pages
File Size : 47,6 Mb
Release : 1995
Category : Science
ISBN : 9810220669

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How Surfaces Intersect in Space by J. Scott Carter Pdf

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 : Peter Giblin
Publisher : Cambridge University Press
Page : 273 pages
File Size : 54,9 Mb
Release : 2010-08-12
Category : Mathematics
ISBN : 9781139491174

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Graphs, Surfaces and Homology by Peter Giblin Pdf

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 : L.Christine Kinsey
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 51,8 Mb
Release : 1997-09-26
Category : Mathematics
ISBN : 0387941029

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Topology of Surfaces by L.Christine Kinsey Pdf

" . . . 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 : V.G. Boltyanskii,V.A. Efremovich
Publisher : Springer Science & Business Media
Page : 153 pages
File Size : 42,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475756043

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Intuitive Combinatorial Topology by V.G. Boltyanskii,V.A. Efremovich Pdf

Topology is a relatively young and very important branch of mathematics, which studies the properties of objects that are preserved through deformations, twistings, and stretchings. This book deals with the topology of curves and surfaces as well as with the fundamental concepts of homotopy and homology, and does this in a lively and well-motivated way. This book is well suited for readers who are interested in finding out what topology is all about.

Author : Alexander Degtyarev,Ilia Itenberg,Viatcheslav Kharlamov
Publisher : Springer
Page : 275 pages
File Size : 49,5 Mb
Release : 2007-05-06
Category : Mathematics
ISBN : 9783540399483

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Real Enriques Surfaces by Alexander Degtyarev,Ilia Itenberg,Viatcheslav Kharlamov Pdf

This is the first attempt of a systematic study of real Enriques surfaces culminating in their classification up to deformation. Simple explicit topological invariants are elaborated for identifying the deformation classes of real Enriques surfaces. Some of theses are new and can be applied to other classes of surfaces or higher-dimensional varieties. Intended for researchers and graduate students in real algebraic geometry it may also interest others who want to become familiar with the field and its techniques. The study relies on topology of involutions, arithmetics of integral quadratic forms, algebraic geometry of surfaces, and the hyperkähler structure of K3-surfaces. A comprehensive summary of the necessary results and techniques from each of these fields is included. Some results are developed further, e.g., a detailed study of lattices with a pair of commuting involutions and a certain class of rational complex surfaces.

Author : Morris W. Hirsch
Publisher : Springer Science & Business Media
Page : 230 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468494495

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Differential Topology by Morris W. Hirsch Pdf

"A very valuable book. In little over 200 pages, it presents a well-organized and surprisingly comprehensive treatment of most of the basic material in differential topology, as far as is accessible without the methods of algebraic topology....There is an abundance of exercises, which supply many beautiful examples and much interesting additional information, and help the reader to become thoroughly familiar with the material of the main text." —MATHEMATICAL REVIEWS

Author : Ethan D. Bloch
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 47,8 Mb
Release : 2011-06-27
Category : Mathematics
ISBN : 9780817681227

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A First Course in Geometric Topology and Differential Geometry by Ethan D. Bloch Pdf

The uniqueness of this text in combining geometric topology and differential geometry lies in its unifying thread: the notion of a surface. With numerous illustrations, exercises and examples, the student comes to understand the relationship of the modern abstract approach to geometric intuition. The text is kept at a concrete level, avoiding unnecessary abstractions, yet never sacrificing mathematical rigor. The book includes topics not usually found in a single book at this level.