Author: Dennis Parnell Sullivan
Publisher:
ISBN:
Category : Geometry
Languages : en
Pages : 476

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Book Description

Author: Dennis P. Sullivan
Publisher: Springer
ISBN: 9781402035111
Category : Mathematics
Languages : en
Pages : 286

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Book Description
The seminal ‘MIT notes’ of Dennis Sullivan were issued in June 1970 and were widely circulated at the time. The notes had a - jor in?uence on the development of both algebraic and geometric topology, pioneering the localization and completion of spaces in homotopy theory, including p-local, pro?nite and rational homotopy theory, le- ing to the solution of the Adams conjecture on the relationship between vector bundles and spherical ?brations, the formulation of the ‘Sullivan conjecture’ on the contractibility of the space of maps from the classifying space of a ?nite group to a ?nite dimensional CW complex, theactionoftheGalois groupoverQofthealgebraicclosureQof Q on smooth manifold structures in pro?nite homotopy theory, the K-theory orientation ofPL manifolds and bundles. Some of this material has been already published by Sullivan him- 1 self: in an article in the Proceedings of the 1970 Nice ICM, and in the 1974 Annals of Mathematics papers Genetics of homotopy theory and the Adams conjecture and The transversality character- 2 istic class and linking cycles in surgery theory . Many of the ideas originating in the notes have been the starting point of subsequent 1 reprinted at the end of this volume 2 joint with John Morgan vii viii 3 developments . However, the text itself retains a unique ?avour of its time, and of the range of Sullivan’s ideas.

Author: P.J. Hilton
Publisher: Springer
ISBN: 3540372687
Category : Mathematics
Languages : en
Pages : 178

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Author: Douglas C. Ravenel
Publisher: Princeton University Press
ISBN: 9780691025728
Category : Mathematics
Languages : en
Pages : 228

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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.

Author: Roman Mikhailov
Publisher: Springer Science & Business Media
ISBN: 3540858172
Category : Mathematics
Languages : en
Pages : 367

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Book Description
A fundamental object of study in group theory is the lower central series of groups. Understanding its relationship with the dimension series is a challenging task. This monograph presents an exposition of different methods for investigating this relationship.

Author: William Browder
Publisher: Princeton University Press
ISBN: 1400882117
Category : Mathematics
Languages : en
Pages : 567

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Book Description
This book contains accounts of talks held at a symposium in honor of John C. Moore in October 1983 at Princeton University, The work includes papers in classical homotopy theory, homological algebra, rational homotopy theory, algebraic K-theory of spaces, and other subjects.

Author: N. H. Kuiper
Publisher: Springer
ISBN: 3540366539
Category : Mathematics
Languages : en
Pages : 240

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Author: Shigeyuki Morita
Publisher: American Mathematical Soc.
ISBN: 0821821393
Category : Mathematics
Languages : en
Pages : 202

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Book Description
Characteristic classes are central to the modern study of the topology and geometry of manifolds. They were first introduced in topology, where, for instance, they could be used to define obstructions to the existence of certain fiber bundles. Characteristic classes were later defined (via the Chern-Weil theory) using connections on vector bundles, thus revealing their geometric side. In the late 1960s new theories arose that described still finer structures. Examples of the so-called secondary characteristic classes came from Chern-Simons invariants, Gelfand-Fuks cohomology, and the characteristic classes of flat bundles. The new techniques are particularly useful for the study of fiber bundles whose structure groups are not finite dimensional. The theory of characteristic classes of surface bundles is perhaps the most developed. Here the special geometry of surfaces allows one to connect this theory to the theory of moduli space of Riemann surfaces, i.e., Teichmüller theory. In this book Morita presents an introduction to the modern theories of characteristic classes.

Author: Shmuel Weinberger
Publisher: Cambridge University Press
ISBN: 1107142598
Category : Mathematics
Languages : en
Pages : 365

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Book Description
Explains, using examples, the central role of the fundamental group in the geometry, global analysis, and topology of manifolds.

Author: F. R. Cohen
Publisher: Springer
ISBN: 3540379851
Category : Mathematics
Languages : en
Pages : 501

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Book Description