Elements Of Combinatorial And Differential Topology PDF Download
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Author | : Viktor Vasilʹevich Prasolov |
Publisher | : American Mathematical Soc. |
Total Pages | : 348 |
Release | : 2006 |
Genre | : Mathematics |
ISBN | : 0821838091 |
Download Elements of Combinatorial and Differential Topology Book in PDF, ePub and Kindle
Modern topology uses very diverse methods. This book is devoted largely to methods of combinatorial topology, which reduce the study of topological spaces to investigations of their partitions into elementary sets, and to methods of differential topology, which deal with smooth manifolds and smooth maps. Many topological problems can be solved by using either of these two kinds of methods, combinatorial or differential. In such cases, both approaches are discussed. One of the maingoals of this book is to advance as far as possible in the study of the properties of topological spaces (especially manifolds) without employing complicated techniques. This distinguishes it from the majority of other books on topology. The book contains many problems; almost all of them are suppliedwith hints or complete solutions.
Author | : V. V. Prasolov |
Publisher | : American Mathematical Society |
Total Pages | : 331 |
Release | : 2022-03-25 |
Genre | : Mathematics |
ISBN | : 1470469448 |
Download Elements of Combinatorial and Differential Topology Book in PDF, ePub and Kindle
Modern topology uses very diverse methods. This book is devoted largely to methods of combinatorial topology, which reduce the study of topological spaces to investigations of their partitions into elementary sets, and to methods of differential topology, which deal with smooth manifolds and smooth maps. Many topological problems can be solved by using either of these two kinds of methods, combinatorial or differential. In such cases, both approaches are discussed. One of the main goals of this book is to advance as far as possible in the study of the properties of topological spaces (especially manifolds) without employing complicated techniques. This distinguishes it from the majority of other books on topology. The book contains many problems; almost all of them are supplied with hints or complete solutions.
Author | : Viktor Vasilʹevich Prasolov |
Publisher | : American Mathematical Soc. |
Total Pages | : 432 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 0821838121 |
Download Elements of Homology Theory Book in PDF, ePub and Kindle
The book is a continuation of the previous book by the author (Elements of Combinatorial and Differential Topology, Graduate Studies in Mathematics, Volume 74, American Mathematical Society, 2006). It starts with the definition of simplicial homology and cohomology, with many examples and applications. Then the Kolmogorov-Alexander multiplication in cohomology is introduced. A significant part of the book is devoted to applications of simplicial homology and cohomology to obstruction theory, in particular, to characteristic classes of vector bundles. The later chapters are concerned with singular homology and cohomology, and Cech and de Rham cohomology. The book ends with various applications of homology to the topology of manifolds, some of which might be of interest to experts in the area. The book contains many problems; almost all of them are provided with hints or complete solutions.
Author | : Anant R. Shastri |
Publisher | : CRC Press |
Total Pages | : 319 |
Release | : 2011-03-04 |
Genre | : Mathematics |
ISBN | : 1439831637 |
Download Elements of Differential Topology Book in PDF, ePub and Kindle
Derived from the author's course on the subject, Elements of Differential Topology explores the vast and elegant theories in topology developed by Morse, Thom, Smale, Whitney, Milnor, and others. It begins with differential and integral calculus, leads you through the intricacies of manifold theory, and concludes with discussions on algebraic topol
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 | : L. S. Pontryagin |
Publisher | : Courier Corporation |
Total Pages | : 112 |
Release | : 2015-05-20 |
Genre | : Mathematics |
ISBN | : 0486406857 |
Download Foundations of Combinatorial Topology Book in PDF, ePub and Kindle
Concise, rigorous introduction to homology theory features applications to dimension theory and fixed-point theorems. Lucid coverage of the field includes examinations of complexes and their Betti groups, invariance of the Betti groups, and continuous mappings and fixed points. Proofs are presented in a complete and careful manner. A beneficial text for a graduate-level course, "this little book is an extremely valuable addition to the literature of algebraic topology." — The Mathematical Gazette.
Author | : John Willard Milnor |
Publisher | : Princeton University Press |
Total Pages | : 80 |
Release | : 1997-12-14 |
Genre | : Mathematics |
ISBN | : 9780691048338 |
Download Topology from the Differentiable Viewpoint Book in PDF, ePub and Kindle
This elegant book by distinguished mathematician John Milnor, provides a clear and succinct introduction to one of the most important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, he goes on to examine tangent spaces, oriented manifolds, and vector fields. Key concepts such as homotopy, the index number of a map, and the Pontryagin construction are discussed. The author presents proofs of Sard's theorem and the Hopf theorem.
Author | : Marston Morse |
Publisher | : |
Total Pages | : 286 |
Release | : 1965 |
Genre | : Combinatorial topology |
ISBN | : |
Download Differential and Combinatorial Topology Book in PDF, ePub and Kindle
Author | : Michael Henle |
Publisher | : Courier Corporation |
Total Pages | : 340 |
Release | : 1994-01-01 |
Genre | : Mathematics |
ISBN | : 9780486679662 |
Download A Combinatorial Introduction to Topology Book in PDF, ePub and Kindle
Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.
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.