Cover of: Stable homotopy and generalised homology | J. Frank Adams

Stable homotopy and generalised homology

  • 373 Pages
  • 0.23 MB
  • 152 Downloads
  • English
by
University of Chicago Press , Chicago
Homotopy theory., Homology theory., Cobordism th
StatementJ. F. Adams.
SeriesChicago lectures in Mathematics
Classifications
LC ClassificationsQA612.7 .A3
The Physical Object
Paginationx, 373 p. ;
ID Numbers
Open LibraryOL5045563M
ISBN 100226005232
LC Control Number74005735

Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in, andthe well-written notes of which are published in this classic in algebraic topology.

The three series focused on Novikov’s work on operations in complex cobordism. The three series focused on Novikov's work on operations in complex cobordism, Quillen's work on formal groups and complex cobordism, and stable homotopy and generalized homology. Adams's exposition of the first two topics played a vital role in setting the stage for modern work on periodicity phenomena in stable homotopy theory.5/5(5).

The three series focused on Novikov's work on operations in complex cobordism, Quillen's work on formal groups and complex cobordism, and stable homotopy and generalized homology.

Adams's. Books J. Adams,Stable Homotopy and Generalised Homology, Univ. of Chicago Press, on stable homotopy theory and generalised homology theory, with emphasis on complex cobordism theory, complex oriented cohomology theory, and the Adams spectral sequence / Adams-Novikov spectral sequence (today: “ chromatic homotopy theory ”).

Consists of three lectures, each meant to be readable on their own, and there is overlap in topics. Starting from stable homotopy groups and (co)homology theories, the authors study the most important categories of spectra and the stable homotopy category, before moving on to computational aspects and more advanced topics such as monoidal structures, localisations and chromatic homotopy theory.

Stable homotopy and generalised homology / J. Adams University of Chicago Press Chicago Wikipedia Citation Please see Wikipedia's template documentation for further.

Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in, andthe well-written notes of which are published in.

Stable homotopy and generalised homology,Adams' blue book. Stable homotopy and generalised homology, Part II, Univ. of Chicago Press, Illinois and London, L Lectures on generalised cohomology, Lecture Notes in Math., vol. 99, Springer-Verlag, Berlin, S Stable homotopy theory, Lecture Notes in Math., vol.

3, Springer-Verlag, Berlin, O. Adams,Stable Homotopy and Generalised Stable homotopy and generalised homology book, Univ.

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of Chicago Press, J. Adams,Infinite Loop Spaces, Ann. of Math. Stud A. AdemandR. Milgram,Cohomology of Finite Groups, Springer-Verlag, The book series Chicago Lectures in Mathematics published or distributed by the University of Chicago Press. Book Series: Chicago Lectures in Mathematics All Chicago e-books are on sale at 30% off with the code EBOOK Adams, J.

F., Stable Homotopy and Generalised Homology, Chicago Lectures in Mathematics (University of Chicago Press, Chicago, IL, ). Reprint of the original.

Reprint of the original. In doing so, it exposes most of the major ideas of the homotopy theory of presheaves of spectra, and generalized etale homology theories in particular. The treatment includes, for the purpose of adequately dealing with cup product structures, a development of stable homotopy theory for n-fold spectra, which is then promoted to the level of.

Nilpotence and Periodicity in Stable Homotopy Theory. Annals of Math Studies Princeton University Press, [$43] • J F Adams. Stable Homotopy and Generalised Homology. University of Chicago Press, [$34] • F Hirzebruch, T Berger, and R Jung.

Appendix A3. Tables of Homotopy Groups of Spheres The Adams spectral sequence for p = 2 below dimension The Adams– Novikov spectral sequence for p = 2 below dimension Comparison of Toda’s, Tangora’s and our notation at p = 2.

3-Primary stable homotopy excluding in J. 5-Primary stable homotopy excluding in J. Bibliography iv.

Description Stable homotopy and generalised homology FB2

Stable homotype and generalized homology. by ADAMS, J.F. and a great selection of related books, art and collectibles available now at - Stable Homotopy and Generalized Homology;chicago Lectures in Mathematics by Adams, J F - AbeBooks Passion for books. Sign On My Account Basket Help.

Homotopy and homology not-so-long exact sequences. Stable homotopy in categorical algebra. Pages Cohen, Joel M. Preview. Spectral sequences and calculation of stable homotopy. Pages Cohen, Joel M.

Preview. Show next xx. Read this book on SpringerLink *immediately available upon purchase as print book shipments may be. From the reviews: "The author has attempted an ambitious and most commendable project. He assumes only a modest knowledge of algebraic topology on the part of the reader to start with, and he leads the reader systematically to the point at which he can begin to tackle problems in the current areas of research centered around generalized homology theories and their applications.

J. Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in, andthe well-written notes of which are published in this classic in algebraic topology.

The three series focused on Novikov's work on operations in Price: $ STABLE ALGEBRAIC TOPOLOGY, – J. MAY Contents 1. Setting up the foundations 3 2. The Eilenberg-Steenrod axioms 4 3. Stable and unstable homotopy groups 5 4.

Spectral sequences and calculations in homology and homotopy 6 5. Steenrod operations, K(π,n)’s, and characteristic classes 8 6. The introduction of cobordism 10 7. The purpose of the book is to give an exposition of generalized (co)homology theories that can be read by a wide group of mathematicians who are not experts in algebraic topology.

It starts with basic notions of homotopy theory and then introduces the axioms of generalized (co)homology theory. ples of generalized homology theories are known; for instance, the stable homotopy groups. Like the homology and cohomology groups, the stable homotopy and cohomotopy groups satisfy Alexander duality [26].

Given a cohomology theory, one might then define the corresponding homology.

Details Stable homotopy and generalised homology EPUB

J.F. Adams, Stable Homotopy and Generalised Homology. A.K. Bousfield, The localization of spectra with respect to homology, Topology 18 () D.C. Ravenel: Complex Cobordism and the Stable Homotopy Groups of Spheres ("Green Book").

Online Edition; D.C. Ravenel: Nilpotence and Periodicity in Stable Homotopy Theory ("Orange Book. Find helpful customer reviews and review ratings for Stable Homotopy and Generalized Homology;Chicago Lectures in Mathematics at Read honest and unbiased product reviews from our users.

Stable homotopy and generalised homology. [John Frank Adams] Home. WorldCat Home About WorldCat Help. Search. Search for Library Items Search for Lists Search for Contacts Search for a Library. Create Book\/a>, schema:CreativeWork\/a> ; \u00A0\u00A0\u00A0\n library. π n (X) = [S n, X] = [S, X] n is the nth stable homotopy group of X.

π * (X) is the sum of the groups π n (X), and is called the coefficient ring of X when X is a ring spectrum.

X∧Y is the smash product of two spectra. If X is a spectrum, then it defines generalized homology and cohomology theories on the category of spectra as follows. Adams. Stable Homotopy and Generalised sity of Chicago Press, Chicago, zbMATH Google Scholar.

There have been a couple questions on MO, and elsewhere, that have made me curious about integral or rational cohomology operations. I feel pretty familiar with the classical Steenrod algebra and its uses and constructions, and I am at a loss as to imagine some chain level construction of such an operation, other than by coupling mod p operations with bockstein and reduction maps.

I am most interested in a class of invariants called (generalized) homology theories. Such theories include classical (ordinary) homology theory, K-theory, cobordism theories, algebraic K-theory, and many more.

A very intriguing example of a homology theory is stable homotopy theory, which is most closely related to homotopy groups. 1. Books • Adams Stable homotopy theory. • Adams Stable homotopy and generalised homology.

• Atiyah K-theory. • Bousfield and Kan, Homotopy limits, completions and localizations. • Elmendorf, Kriz, Mandell, and May, Rings, modules, and algebras in stable homotopy theory. • May, Geometry of iterated loop spaces. Book Description. The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines.

The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has.We can define the (stable) homotopy groups of a spectrum to be those given by = [,], where is the sphere spectrum and [,] is the set of homotopy classes of maps from define the generalized homology theory of a spectrum E by = (∧) = [, ∧] and define its generalized cohomology theory by = [−,].

Here can be a spectrum or (by using its suspension spectrum) a space.