Author: Ib H. MadsenPublisher: Cambridge University Press
ISBN: 9780521589567
Category : Mathematics
Languages : en
Pages : 302
Book Description
An introductory textbook on cohomology and curvature with emphasis on applications.
From Calculus to Cohomology
Author: Ib H. MadsenPublisher: Cambridge University Press
ISBN: 9780521589567
Category : Mathematics
Languages : en
Pages : 302
Book Description
An introductory textbook on cohomology and curvature with emphasis on applications.
Rational Homotopy Theory
Author: Yves FelixPublisher: Springer Science & Business Media
ISBN: 0387950680
Category : Mathematics
Languages : en
Pages : 589
Book Description
This is a long awaited book on rational homotopy theory which contains all the main theorems with complete proofs, and more elementary proofs for many results that were proved ten or fifteen years ago. The authors added a frist section on classical algebraic topology to make the book accessible to students with only little background in algebraic topology.
Local Homotopy Theory
Author: John F. JardinePublisher: Springer
ISBN: 1493923005
Category : Mathematics
Languages : en
Pages : 508
Book Description
This monograph on the homotopy theory of topologized diagrams of spaces and spectra gives an expert account of a subject at the foundation of motivic homotopy theory and the theory of topological modular forms in stable homotopy theory. Beginning with an introduction to the homotopy theory of simplicial sets and topos theory, the book covers core topics such as the unstable homotopy theory of simplicial presheaves and sheaves, localized theories, cocycles, descent theory, non-abelian cohomology, stacks, and local stable homotopy theory. A detailed treatment of the formalism of the subject is interwoven with explanations of the motivation, development, and nuances of ideas and results. The coherence of the abstract theory is elucidated through the use of widely applicable tools, such as Barr's theorem on Boolean localization, model structures on the category of simplicial presheaves on a site, and cocycle categories. A wealth of concrete examples convey the vitality and importance of the subject in topology, number theory, algebraic geometry, and algebraic K-theory. Assuming basic knowledge of algebraic geometry and homotopy theory, Local Homotopy Theory will appeal to researchers and advanced graduate students seeking to understand and advance the applications of homotopy theory in multiple areas of mathematics and the mathematical sciences.
Nilpotence and Periodicity in Stable Homotopy Theory
Author: Douglas C. RavenelPublisher: Princeton University Press
ISBN: 9780691025728
Category : Mathematics
Languages : en
Pages : 228
Book Description
Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic. Ravenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic p are introduced. The latter portion of the book provides specialists with a coherent and rigorous account of the proofs. It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.
Groups of Homotopy Spheres, I
Author: M. A. KervairePublisher:
ISBN: 9781021177575
Category : History
Languages : en
Pages : 0
Book Description
Equivariant Stable Homotopy Theory
Author: L. Gaunce Jr. LewisPublisher: Springer
ISBN: 3540470778
Category : Mathematics
Languages : en
Pages : 548
Book Description
This book is a foundational piece of work in stable homotopy theory and in the theory of transformation groups. It may be roughly divided into two parts. The first part deals with foundations of (equivariant) stable homotopy theory. A workable category of CW-spectra is developed. The foundations are such that an action of a compact Lie group is considered throughout, and spectra allow desuspension by arbitrary representations. But even if the reader forgets about group actions, he will find many details of the theory worked out for the first time. More subtle constructions like smash products, function spectra, change of group isomorphisms, fixed point and orbit spectra are treated. While it is impossible to survey properly the material which is covered in the book, it does boast these general features: (i) a thorough and reliable presentation of the foundations of the theory; (ii) a large number of basic results, principal applications, and fundamental techniques presented for the first time in a coherent theory, unifying numerous treatments of special cases in the literature.
Cubical Homotopy Theory
Author: Brian A. MunsonPublisher: Cambridge University Press
ISBN: 1107030250
Category : Mathematics
Languages : en
Pages : 649
Book Description
A modern, example-driven introduction to cubical diagrams and related topics such as homotopy limits and cosimplicial spaces.
Homotopy Theory of Schemes
Author: Fabien MorelPublisher: American Mathematical Soc.
ISBN: 9780821831649
Category : Mathematics
Languages : en
Pages : 116
Book Description
In this text, the author presents a general framework for applying the standard methods from homotopy theory to the category of smooth schemes over a reasonable base scheme $k$. He defines the homotopy category $h(\mathcal{E} k)$ of smooth $k$-schemes and shows that it plays the same role for smooth $k$-schemes as the classical homotopy category plays for differentiable varieties. It is shown that certain expected properties are satisfied, for example, concerning the algebraic$K$-theory of those schemes. In this way, advanced methods of algebraic topology become available in modern algebraic geometry.
Motivic Homotopy Theory
Author: Bjorn Ian DundasPublisher: Springer Science & Business Media
ISBN: 3540458972
Category : Mathematics
Languages : en
Pages : 228
Book Description
This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Aimed at graduate students in algebraic topology and algebraic geometry, it contains background material from both of these fields, as well as the foundations of motivic homotopy theory. It will serve as a good introduction as well as a convenient reference for a broad group of mathematicians to this important and fascinating new subject. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject.
Manifolds of Differentiable Mappings
Author: Peter W. MichorPublisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 176
Book Description