Introduction To Differential And Algebraic Topology PDF Download
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Author | : Matthias Kreck |
Publisher | : American Mathematical Soc. |
Total Pages | : 234 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 0821848984 |
Download Differential Algebraic Topology Book in PDF, ePub and Kindle
This book presents a geometric introduction to the homology of topological spaces and the cohomology of smooth manifolds. The author introduces a new class of stratified spaces, so-called stratifolds. He derives basic concepts from differential topology such as Sard's theorem, partitions of unity and transversality. Based on this, homology groups are constructed in the framework of stratifolds and the homology axioms are proved. This implies that for nice spaces these homology groups agree with ordinary singular homology. Besides the standard computations of homology groups using the axioms, straightforward constructions of important homology classes are given. The author also defines stratifold cohomology groups following an idea of Quillen. Again, certain important cohomology classes occur very naturally in this description, for example, the characteristic classes which are constructed in the book and applied later on. One of the most fundamental results, Poincare duality, is almost a triviality in this approach. Some fundamental invariants, such as the Euler characteristic and the signature, are derived from (co)homology groups. These invariants play a significant role in some of the most spectacular results in differential topology. In particular, the author proves a special case of Hirzebruch's signature theorem and presents as a highlight Milnor's exotic 7-spheres. This book is based on courses the author taught in Mainz and Heidelberg. Readers should be familiar with the basic notions of point-set topology and differential topology. The book can be used for a combined introduction to differential and algebraic topology, as well as for a quick presentation of (co)homology in a course about differential geometry.
Author | : Yu.G. Borisovich |
Publisher | : Springer Science & Business Media |
Total Pages | : 500 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 9401719594 |
Download Introduction to Differential and Algebraic Topology Book in PDF, ePub and Kindle
Topology as a subject, in our opinion, plays a central role in university education. It is not really possible to design courses in differential geometry, mathematical analysis, differential equations, mechanics, functional analysis that correspond to the temporary state of these disciplines without involving topological concepts. Therefore, it is essential to acquaint students with topo logical research methods already in the first university courses. This textbook is one possible version of an introductory course in topo logy and elements of differential geometry, and it absolutely reflects both the authors' personal preferences and experience as lecturers and researchers. It deals with those areas of topology and geometry that are most closely related to fundamental courses in general mathematics. The educational material leaves a lecturer a free choice in designing his own course or his own seminar. We draw attention to a number of particularities in our book. The first chap ter, according to the authors' intention, should acquaint readers with topolo gical problems and concepts which arise from problems in geometry, analysis, and physics. Here, general topology (Ch. 2) is presented by introducing con structions, for example, related to the concept of quotient spaces, much earlier than various other notions of general topology thus making it possible for students to study important examples of manifolds (two-dimensional surfaces, projective spaces, orbit spaces, etc.) as topological spaces, immediately.
Author | : Raoul Bott |
Publisher | : Springer Science & Business Media |
Total Pages | : 319 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 1475739516 |
Download Differential Forms in Algebraic Topology Book in PDF, ePub and Kindle
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 | : Theodor Bröcker |
Publisher | : Cambridge University Press |
Total Pages | : 176 |
Release | : 1982-09-16 |
Genre | : Mathematics |
ISBN | : 9780521284707 |
Download Introduction to Differential Topology Book in PDF, ePub and Kindle
This book is intended as an elementary introduction to differential manifolds. The authors concentrate on the intuitive geometric aspects and explain not only the basic properties but also teach how to do the basic geometrical constructions. An integral part of the work are the many diagrams which illustrate the proofs. The text is liberally supplied with exercises and will be welcomed by students with some basic knowledge of analysis and topology.
Author | : M. Karoubi |
Publisher | : Cambridge University Press |
Total Pages | : 380 |
Release | : 1987 |
Genre | : Mathematics |
ISBN | : 9780521317146 |
Download Algebraic Topology Via Differential Geometry Book in PDF, ePub and Kindle
In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples. Topics covered include Mayer-Vietoris exact sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This book will be suitable for graduate students taking courses in algebraic topology and in differential topology. Mathematicians studying relativity and mathematical physics will find this an invaluable introduction to the techniques of differential geometry.
Author | : Morris W. Hirsch |
Publisher | : Springer Science & Business Media |
Total Pages | : 230 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 146849449X |
Download Differential Topology Book in PDF, ePub and Kindle
"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 | : Andrew H. Wallace |
Publisher | : Courier Corporation |
Total Pages | : 212 |
Release | : 2007-02-27 |
Genre | : Mathematics |
ISBN | : 0486457869 |
Download An Introduction to Algebraic Topology Book in PDF, ePub and Kindle
Originally published: Homology theory on algebraic varieties. New York: Pergamon Press, 1957.
Author | : Jean Dieudonné |
Publisher | : Springer Science & Business Media |
Total Pages | : 666 |
Release | : 2009-09-01 |
Genre | : Mathematics |
ISBN | : 0817649077 |
Download A History of Algebraic and Differential Topology, 1900 - 1960 Book in PDF, ePub and Kindle
This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it! —MathSciNet
Author | : John M. Lee |
Publisher | : Springer Science & Business Media |
Total Pages | : 395 |
Release | : 2006-04-06 |
Genre | : Mathematics |
ISBN | : 038722727X |
Download Introduction to Topological Manifolds Book in PDF, ePub and Kindle
Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.
Author | : Edmond A. Jonckheere |
Publisher | : Oxford University Press, USA |
Total Pages | : 625 |
Release | : 1997 |
Genre | : Algebraic topology |
ISBN | : 0195093011 |
Download Algebraic and Differential Topology of Robust Stability Book in PDF, ePub and Kindle
In this book, two seemingly unrelated fields - algebraic topology and robust control - are brought together. The book develops algebraic/differential topology proceeding from an easily motivated control engineering problem, showing the relevance of advanced topological concepts and reconstructing the fundamental concepts of algebraic/differential topology from an application-oriented point of view. It is suitable for graduate students in engineering and/or applied mathematics, and academic researchers.