Topologia Differenziale
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Topologia Differenziale
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Author : E. Vesentini
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-27
Topologia Differenziale written by E. Vesentini and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-27 with Mathematics categories.
J. Cerf: Invariants des paires d ́espaces. Applications à la topologie differentielle.- A. Häfliger: Variétés feuilletées.- M.A. Kervaire: La méthode de Pontryagin pour la classification des applications sur une sphère.- S. Smale: Stable manifolds for differential equations and diffeomorphisms.
Differential Topology
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Author : Victor Guillemin
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Differential Topology written by Victor Guillemin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
Differential Topology provides an elementary and intuitive introduction to the study of smooth manifolds. In the years since its first publication, Guillemin and Pollack's book has become a standard text on the subject. It is a jewel of mathematical exposition, judiciously picking exactly the right mixture of detail and generality to display the richness within. The text is mostly self-contained, requiring only undergraduate analysis and linear algebra. By relying on a unifying idea--transversality--the authors are able to avoid the use of big machinery or ad hoc techniques to establish the main results. In this way, they present intelligent treatments of important theorems, such as the Lefschetz fixed-point theorem, the Poincaré-Hopf index theorem, and Stokes theorem. The book has a wealth of exercises of various types. Some are routine explorations of the main material. In others, the students are guided step-by-step through proofs of fundamental results, such as the Jordan-Brouwer separation theorem. An exercise section in Chapter 4 leads the student through a construction of de Rham cohomology and a proof of its homotopy invariance. The book is suitable for either an introductory graduate course or an advanced undergraduate course.
Differential Topology
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Author : Morris W. Hirsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Differential Topology written by Morris W. Hirsch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
"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
Topologia Differenziale
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Author : E. Vesentini
language : fr
Publisher:
Release Date : 2011-07-21
Topologia Differenziale written by E. Vesentini and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-21 with categories.
Elements Of Combinatorial And Differential Topology
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Author : Viktor Vasilʹevich Prasolov
language : en
Publisher: American Mathematical Soc.
Release Date :
Elements Of Combinatorial And Differential Topology written by Viktor Vasilʹevich Prasolov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
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.
Differential Algebraic Topology
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Author : Matthias Kreck
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Differential Algebraic Topology written by Matthias Kreck and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
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.
Elements Of Combinatorial And Differential Topology
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Author : V. V. Prasolov
language : en
Publisher: American Mathematical Society
Release Date : 2022-03-25
Elements Of Combinatorial And Differential Topology written by V. V. Prasolov and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-25 with Mathematics categories.
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.
Algebraic And Differential Topology
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Author : R.V. Gamkrelidze
language : en
Publisher: Routledge
Release Date : 2022-01-27
Algebraic And Differential Topology written by R.V. Gamkrelidze and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-27 with Mathematics categories.
Algebraic and Differential Topology presents in a clear, concise, and detailed manner the fundamentals of homology theory. It first defines the concept of a complex and its Betti groups, then discusses the topolgoical invariance of a Betti group. The book next presents various applications of homology theory, such as mapping of polyhedrons onto other polyhedrons as well as onto themselves. The third volume in L.S. Pontryagin's Selected Works, this book provides as many insights into algebraic topology for today's mathematician as it did when the author was making his initial endeavors into this field.
Elementary Differential Topology Am 54 Volume 54
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Author : James R. Munkres
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Elementary Differential Topology Am 54 Volume 54 written by James R. Munkres and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
The description for this book, Elementary Differential Topology. (AM-54), Volume 54, will be forthcoming.
Synthetic Differential Topology
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Author : Marta Bunge
language : en
Publisher: Cambridge University Press
Release Date : 2018-03-29
Synthetic Differential Topology written by Marta Bunge and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-29 with Mathematics categories.
Represents the state of the art in the new field of synthetic differential topology.