A First Course In Algebraic Topology

Author : Czes Kosniowski
Publisher : Cambridge University Press
Page : 284 pages
File Size : 40,6 Mb
Release : 1980-09-25
Category : Mathematics
ISBN : 0521231957

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A First Course in Algebraic Topology by Czes Kosniowski Pdf

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.

Author : C. KOSNIOWSKI
Publisher : Unknown
Page : 0 pages
File Size : 42,5 Mb
Release : 1980
Category : Electronic
ISBN : 0512231958

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FIRST COURSE IN ALGEBRAIC TOPOLOGY. by C. KOSNIOWSKI Pdf

Author : William Fulton
Publisher : Springer Science & Business Media
Page : 435 pages
File Size : 44,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461241805

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Algebraic Topology by William Fulton Pdf

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

Author : J. P. May
Publisher : University of Chicago Press
Page : 262 pages
File Size : 51,7 Mb
Release : 1999-09
Category : Mathematics
ISBN : 0226511839

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A Concise Course in Algebraic Topology by J. P. May Pdf

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.

Author : A. Lahiri,B. K. Lahiri
Publisher : Alpha Science Int'l Ltd.
Page : 132 pages
File Size : 42,8 Mb
Release : 2000
Category : Mathematics
ISBN : 1842650033

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A First Course in Algebraic Topology by A. Lahiri,B. K. Lahiri Pdf

This volume is an introductory text where the subject matter has been presented lucidly so as to help self study by the beginners. New definitions are followed by suitable illustrations and the proofs of the theorems are easily accessible to the readers. Sufficient number of examples have been incorporated to facilitate clear understanding of the concepts. The book starts with the basic notions of category, functors and homotopy of continuous mappings including relative homotopy. Fundamental groups of circles and torus have been treated along with the fundamental group of covering spaces. 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.

Author : Marvin J. Greenberg
Publisher : CRC Press
Page : 231 pages
File Size : 42,6 Mb
Release : 2018-03-05
Category : Mathematics
ISBN : 9780429982033

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Algebraic Topology by Marvin J. Greenberg Pdf

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

Author : William S. Massey
Publisher : Springer
Page : 448 pages
File Size : 51,8 Mb
Release : 2019-06-28
Category : Mathematics
ISBN : 9781493990634

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A Basic Course in Algebraic Topology by William S. Massey Pdf

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.

Author : J. P. May,K. Ponto
Publisher : University of Chicago Press
Page : 544 pages
File Size : 45,6 Mb
Release : 2012-02
Category : Mathematics
ISBN : 9780226511788

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More Concise Algebraic Topology by J. P. May,K. Ponto Pdf

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.

Author : Allen Hatcher
Publisher : Cambridge University Press
Page : 572 pages
File Size : 52,7 Mb
Release : 2002
Category : Mathematics
ISBN : 0521795400

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Algebraic Topology by Allen Hatcher Pdf

An introductory textbook suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises.

Author : F.H. Croom
Publisher : Springer Science & Business Media
Page : 187 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468494754

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Basic Concepts of Algebraic Topology by F.H. Croom Pdf

This text is intended as a one semester introduction to algebraic topology at the undergraduate and beginning graduate levels. Basically, it covers simplicial homology theory, the fundamental group, covering spaces, the higher homotopy groups and introductory singular homology theory. The text follows a broad historical outline and uses the proofs of the discoverers of the important theorems when this is consistent with the elementary level of the course. This method of presentation is intended to reduce the abstract nature of algebraic topology to a level that is palatable for the beginning student and to provide motivation and cohesion that are often lacking in abstact treatments. The text emphasizes the geometric approach to algebraic topology and attempts to show the importance of topological concepts by applying them to problems of geometry and analysis. The prerequisites for this course are calculus at the sophomore level, a one semester introduction to the theory of groups, a one semester introduc tion to point-set topology and some familiarity with vector spaces. Outlines of the prerequisite material can be found in the appendices at the end of the text. It is suggested that the reader not spend time initially working on the appendices, but rather that he read from the beginning of the text, referring to the appendices as his memory needs refreshing. The text is designed for use by college juniors of normal intelligence and does not require "mathematical maturity" beyond the junior level.

Author : Joe Harris
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 51,9 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475721898

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Algebraic Geometry by Joe Harris Pdf

"This book succeeds brilliantly by concentrating on a number of core topics...and by treating them in a hugely rich and varied way. The author ensures that the reader will learn a large amount of classical material and perhaps more importantly, will also learn that there is no one approach to the subject. The essence lies in the range and interplay of possible approaches. The author is to be congratulated on a work of deep and enthusiastic scholarship." --MATHEMATICAL REVIEWS

Author : Holger Kammeyer
Publisher : Springer Nature
Page : 186 pages
File Size : 41,5 Mb
Release : 2022-06-20
Category : Mathematics
ISBN : 9783030983130

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Introduction to Algebraic Topology by Holger Kammeyer Pdf

This textbook provides a succinct introduction to algebraic topology. It follows a modern categorical approach from the beginning and gives ample motivation throughout so that students will find this an ideal first encounter to the field. Topics are treated in a self-contained manner, making this a convenient resource for instructors searching for a comprehensive overview of the area. It begins with an outline of category theory, establishing the concepts of functors, natural transformations, adjunction, limits, and colimits. As a first application, van Kampen's theorem is proven in the groupoid version. Following this, an excursion to cofibrations and homotopy pushouts yields an alternative formulation of the theorem that puts the computation of fundamental groups of attaching spaces on firm ground. Simplicial homology is then defined, motivating the Eilenberg-Steenrod axioms, and the simplicial approximation theorem is proven. After verifying the axioms for singular homology, various versions of the Mayer-Vietoris sequence are derived and it is shown that homotopy classes of self-maps of spheres are classified by degree.The final chapter discusses cellular homology of CW complexes, culminating in the uniqueness theorem for ordinary homology. Introduction to Algebraic Topology is suitable for a single-semester graduate course on algebraic topology. It can also be used for self-study, with numerous examples, exercises, and motivating remarks included.

Author : Raoul Bott,Loring W. Tu
Publisher : Springer Science & Business Media
Page : 319 pages
File Size : 51,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475739510

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Differential Forms in Algebraic Topology by Raoul Bott,Loring W. Tu Pdf

Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.

Author : Tammo tom Dieck
Publisher : European Mathematical Society
Page : 584 pages
File Size : 51,5 Mb
Release : 2008
Category : Mathematics
ISBN : 3037190485

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Algebraic Topology by Tammo tom Dieck Pdf

This book is written as a textbook on algebraic topology. The first part covers the material for two introductory courses about homotopy and homology. The second part presents more advanced applications and concepts (duality, characteristic classes, homotopy groups of spheres, bordism). The author recommends starting an introductory course with homotopy theory. For this purpose, classical results are presented with new elementary proofs. Alternatively, one could start more traditionally with singular and axiomatic homology. Additional chapters are devoted to the geometry of manifolds, cell complexes and fibre bundles. A special feature is the rich supply of nearly 500 exercises and problems. Several sections include topics which have not appeared before in textbooks as well as simplified proofs for some important results. Prerequisites are standard point set topology (as recalled in the first chapter), elementary algebraic notions (modules, tensor product), and some terminology from category theory. The aim of the book is to introduce advanced undergraduate and graduate (master's) students to basic tools, concepts and results of algebraic topology. Sufficient background material from geometry and algebra is included.

Author : Sze-Tsen Hu
Publisher : Unknown
Page : 270 pages
File Size : 50,8 Mb
Release : 1966
Category : Homology theory
ISBN : STANFORD:36105031468080

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Homology Theory by Sze-Tsen Hu Pdf