Author: Czes Kosniowski

Publisher: CUP Archive

ISBN: 9780521298643

Category: Mathematics

Page: 269

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### A First Course in Algebraic Topology

This self-contained introduction to algebraic topology is suitable for a number of topology courses. It consists of about one quarter 'general topology' (without its usual pathologies) and three quarters 'algebraic topology' (centred around the fundamental group, a readily grasped topic which gives a good idea of what algebraic topology is). The book has emerged from courses given at the University of Newcastle-upon-Tyne to senior undergraduates and beginning postgraduates. It has been written at a level which will enable the reader to use it for self-study as well as a course book. The approach is leisurely and a geometric flavour is evident throughout. The many illustrations and over 350 exercises will prove invaluable as a teaching aid. This account will be welcomed by advanced students of pure mathematics at colleges and universities.

### Algebraic Topology

To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ ential topology, etc.), we concentrate our attention on concrete prob lems in low dimensions, introducing only as much algebraic machin ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel opment of the subject. What would we like a student to know after a first course in to pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind ing numbers and degrees of mappings, fixed-point theorems; appli cations such as the Jordan curve theorem, invariance of domain; in dices of vector fields and Euler characteristics; fundamental groups

### A First Course in Algebraic Topology

Includes basic notions of category, functors and homotopy of continuous mappings including relative homotopy. In this book, simplexes and complexes are presented in detail and two homology theories-simplicial homology and singular homology have been considered along with calculations of some homology groups.

### A Basic Course in Algebraic Topology

This textbook is intended for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unnecessary definitions, terminology, and technical machinery. The text consists of material from the first five chapters of the author's earlier book, Algebraic Topology; an Introduction (GTM 56) together with almost all of his book, Singular Homology Theory (GTM 70). The material from the two earlier books has been substantially revised, corrected, and brought up to date.

### A First Course in Topology

How many dimensions does our universe require for a comprehensive physical description? In 1905, Poincare argued philosophically about the necessity of the three familiar dimensions, while recent research is based on 11 dimensions or even 23 dimensions. The notion of dimension itself presented a basic problem to the pioneers of topology. Cantor asked if dimension was a topological feature of Euclidean space. To answer this question, some important topological ideas were introduced by Brouwer, giving shape to a subject whose development dominated the twentieth century. The basic notions in topology are varied and a comprehensive grounding in point-set topology, the definition and use of the fundamental group, and the beginnings of homology theory requires considerable time.The goal of this book is a focused introduction through these classical topics, aiming throughout at the classical result of the Invariance of Dimension. This text is based on the author's course given at Vassar College and is intended for advanced undergraduate students. It is suitable for a semester-long course on topology for students who have studied real analysis and linear algebra. It is also a good choice for a capstone course, senior seminar, or independent study.

### A Concise Course in Algebraic Topology

Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.

### Algebraic topology

### A First Course in Geometric Topology and Differential Geometry

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.

### Algebraic Topology

### Algebraic Topology

Great first book on algebraic topology. Introduces (co)homology through singular theory.

### An Introduction to Algebraic Topology

A clear exposition, with exercises, of the basic ideas of algebraic topology. Suitable for a two-semester course at the beginning graduate level, it assumes a knowledge of point set topology and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced.

### Introduction to Homotopy Theory

This text is based on a one-semester graduate course taught by the author at The Fields Institute in fall 1995 as part of the homotopy theory program which constituted the Institute's major program that year. The intent of the course was to bring graduate students who had completed a first course in algebraic topology to the point where they could understand research lectures in homotopy theory and to prepare them for the other, more specialized graduate courses being held in conjunction with the program. The notes are divided into two parts: prerequisites and the course proper. Part I, the prerequisites, contains a review of material often taught in a first course in algebraic topology. It should provide a useful summary for students and non-specialists who are interested in learning the basics of algebraic topology. Included are some basic category theory, point set topology, the fundamental group, homological algebra, singular and cellular homology, and Poincare duality. Part II covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets, fiber bundles, Hopf algebras, spectral sequences, localization, generalized homology and cohomology operations. This book collects in one place the material that a researcher in algebraic topology must know. The author has attempted to make this text a self-contained exposition. Precise statements and proofs are given of ``folk'' theorems which are difficult to find or do not exist in the literature.

### More Concise Algebraic Topology

With firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. There are very few textbooks that treat fundamental topics beyond a first course, and many topics now essential to the field are not treated in any textbook. J. Peter May’s A Concise Course in Algebraic Topology addresses the standard first course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and cohomology. In this sequel, May and his coauthor, Kathleen Ponto, cover topics that are essential for algebraic topologists and others interested in algebraic topology, but that are not treated in standard texts. They focus on the localization and completion of topological spaces, model categories, and Hopf algebras. The first half of the book sets out the basic theory of localization and completion of nilpotent spaces, using the most elementary treatment the authors know of. It makes no use of simplicial techniques or model categories, and it provides full details of other necessary preliminaries. With these topics as motivation, most of the second half of the book sets out the theory of model categories, which is the central organizing framework for homotopical algebra in general. Examples from topology and homological algebra are treated in parallel. A short last part develops the basic theory of bialgebras and Hopf algebras.

### A First Course in Topology

Students must prove all of the theorems in this undergraduate-level text, which focuses on point-set topology and emphasizes continuity. The final chapter explores homotopy and the fundamental group. 1975 edition.

### A User's Guide to Algebraic Topology

This book arose from courses taught by the authors, and is designed for both instructional and reference use during and after a first course in algebraic topology. It is a handbook for users who want to calculate, but whose main interests are in applications using the current literature, rather than in developing the theory. Typical areas of applications are differential geometry and theoretical physics. We start gently, with numerous pictures to illustrate the fundamental ideas and constructions in homotopy theory that are needed in later chapters. We show how to calculate homotopy groups, homology groups and cohomology rings of most of the major theories, exact homotopy sequences of fibrations, some important spectral sequences, and all the obstructions that we can compute from these. Our approach is to mix illustrative examples with those proofs that actually develop transferable calculational aids. We give extensive appendices with notes on background material, extensive tables of data, and a thorough index. Audience: Graduate students and professionals in mathematics and physics.

### A First Course in Abstract Algebra

### A First Course in Computational Algebraic Geometry

A quick guide to computing in algebraic geometry with many explicit computational examples introducing the computer algebra system Singular.

### Lecture Notes in Algebraic Topology

### Riemann Surfaces and Algebraic Curves

Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.

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Author: Czes Kosniowski

Publisher: CUP Archive

ISBN: 9780521298643

Category: Mathematics

Page: 269

View: 9452

*A First Course*

Author: William Fulton

Publisher: Springer Science & Business Media

ISBN: 1461241804

Category: Mathematics

Page: 430

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Author: B. K. Lahiri

Publisher: Alpha Science International Limited

ISBN: 9781842652268

Category: Mathematics

Page: 130

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Author: William S. Massey

Publisher: Springer Science & Business Media

ISBN: 9780387974309

Category: Mathematics

Page: 428

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*Continuity and Dimension*

Author: John McCleary

Publisher: American Mathematical Soc.

ISBN: 0821838849

Category: Mathematics

Page: 211

View: 9095

Author: J. P. May

Publisher: University of Chicago Press

ISBN: 9780226511832

Category: Mathematics

Page: 243

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*a first course*

Author: Max K. Agoston

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 360

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Author: Ethan D. Bloch

Publisher: Springer Science & Business Media

ISBN: 0817681221

Category: Mathematics

Page: 421

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Author: N.A

Publisher: 清华大学出版社有限公司

ISBN: 9787302105886

Category: Algebraic topology

Page: 544

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*A First Course*

Author: Marvin J. Greenberg

Publisher: CRC Press

ISBN: 0429970951

Category: Mathematics

Page: 332

View: 7252

Author: Joseph J. Rotman

Publisher: Springer Science & Business Media

ISBN: 1461245761

Category: Mathematics

Page: 437

View: 9567

Author: Paul Selick

Publisher: American Mathematical Soc.

ISBN: 9780821844366

Category: Mathematics

Page: 188

View: 6348

*Localization, Completion, and Model Categories*

Author: J. P. May,K. Ponto

Publisher: University of Chicago Press

ISBN: 0226511782

Category: Mathematics

Page: 514

View: 3173

*An Introduction to Mathematical Thinking*

Author: Robert A Conover

Publisher: Courier Corporation

ISBN: 0486791726

Category: Mathematics

Page: 272

View: 4493

Author: C.T. Dodson,Phillip E. Parker,P.E. Parker

Publisher: Springer Science & Business Media

ISBN: 9780792342939

Category: Mathematics

Page: 410

View: 873

Author: John B. Fraleigh

Publisher: Pearson Education India

ISBN: 9788177589009

Category: Algebra

Page: 520

View: 2207

Author: Wolfram Decker,Gerhard Pfister

Publisher: Cambridge University Press

ISBN: 1107612535

Category: Computers

Page: 118

View: 2311

Author: James F. Davis and Paul Kirk

Publisher: American Mathematical Soc.

ISBN: 9780821872208

Category:

Page: N.A

View: 1869

*A First Course in Hurwitz Theory*

Author: Renzo Cavalieri,Eric Miles

Publisher: Cambridge University Press

ISBN: 1316798933

Category: Mathematics

Page: N.A

View: 5002