Nilpotence and periodicity in stable homotopy theory by Douglas C. Ravenel

Cover of: Nilpotence and periodicity in stable homotopy theory | Douglas C. Ravenel

Published by Princeton University Press in Princeton, N.J .

Written in English

Read online

Subjects:

  • Homotopy theory.

Edition Notes

Includes bibliographical references (p. 195-204) and index.

Book details

Statementby Douglas C. Ravenel.
SeriesAnnals of mathematics studies ;, no. 128
Classifications
LC ClassificationsQA612.7 .R38 1992
The Physical Object
Paginationxiv, 209 p. ;
Number of Pages209
ID Numbers
Open LibraryOL1723237M
ISBN 10069102572X, 069108792X
LC Control Number92026785

Download Nilpotence and periodicity in stable homotopy theory

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 and proved by Devinatz, Hopkins, and Smith in Cited by: 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 and proved by Devinatz, Hopkins, and Smith in The aim of this chapter is to state the nilpotence and period-icity theorems ( and ) with as little technical fussing as possible.

Readers familiar with homotopy theory can skip the rst three sections, which contain some very elementary de nitions. Homotopy A basic problem in homotopy theory is to classify continuous maps up to homotopy. Nilpotence and Periodicity in Stable Homotopy Theorydescribes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in and proved by Devinatz, Hopkins, and Smith in During the last ten years a number of significant advances have been made in homotopy theory, and this book fills.

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.

Describes some major advances made in algebraic topology, centering on the nilpotence and periodicity theorems. This book begins with some elementary concepts of homotopy theory that are needed to state the problem. The latter portion provides specialists with a. Describes major advances made in algebraic topology in recent years, focusing on the nilpotence and periodicity theorems, which were conjectured by the author in and proved by Devinatz, Hopkins and Smith in A number of significant developments in homotopy theory.

structure of stable homotopy theory in the large. The theory was organized around a family of \higher periodicities" generalizing Bott periodicity, and depended on being able to determine the nilpotent and non-nilpotent maps in the category of spectra.

There are three senses in which a map of spectra can be nilpotent: De nition 1. i) A map of. Ravenel, Douglas C. Nilpotence and Periodicity in Stable Homotopy Theory. (AM), Volume Complex Cobordism and Stable Homotopy Groups of Spheres (green book).

Douglas Ravenel. Nilpotence and periodicity in stable homotopy theory (orange book). Douglas Ravenel. Localization with respect to certain periodic homology theories. Ethan Devinatz, Michael Hopkins, Jeffrey Smith. Nilpotence and Stable Homotopy Theory I, II.

Aldridge Bousfield. MATH Nilpotence and Periodicity in Stable Homotopy Theory Second half of Fall (October 22 - December 12) Instructor: Vesna Stojanoska Course description: One of the basic and motivating objects of study in algebraic topology are the stable homotopy groups of spheres, which are the endomorphisms of the unit object in the stable homotopy.

Axiomatic stable homotopy theory About this Title. Mark Hovey, John H. Palmieri and Neil P. Strickland. Publication: Memoirs of the American Mathematical Society Publication Year VolumeNumber ISBNs: (print); (online)Cited by: Nilpotence and stable homotopy theory I By ETHAN S.

DEVINATZ, MICHAEL J. HOPKINS and JEFFREY H. SMITH In the course of his work on the J homomorphism [1] Adams produced for each prime p a self-map a: *PMP Mp of the mod(p) Moore spectrum.

Here kp = 2p-2 if p is odd while k2 = 8, and Mp is the cofibre of the degree p map p: S0 - S 0. 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.

This comprehensive introduction to stable homotopy theory changes that. It presents the foundations of the subject together in one place for the first time, from the motivating phenomena to the modern theory, at a level suitable for those with only a first course in algebraic : David Barnes, Constanze Roitzheim.

The Periodicity Theorem, Talk 1 Vitaly Lorman Octo Note: These are my notes on part of chapter 6 of Ravenel’s Orange Book (Nilpotence and Periodicity in Stable Homotopy Theory), prepared for a talk in the graduate student topology seminar at Johns Hopkins.

Jon Beardsley gave a talk on the rst part of chapter. This book is a compilation of lecture notes that were prepared for the graduate course “Adams Spectral Sequences and Stable Homotopy Theory” given at The Fields Institute during the fall of The aim of this volume is to prepare students with a knowledge of elementary algebraic topology to study recent developments in stable homotopy.

NILPOTENCE IN STABLE HOMOTOPY THEORY RICHARD WONG Abstract. This talk covers most of section 4 in the Mathew-Naumann-Noel paper [MNN15]. We rst discuss nilpotence in an arbitrary symmetric monoidal stable 1-category.

We then discuss the historical origins of nilpotence in the stable homotopy category, namely the Ravenel conjectures and the.

Title: Nilpotence and descent in equivariant stable homotopy theory Authors: Akhil Mathew, Niko Naumann, Justin Noel (Submitted on 24 Jul ( Cited by: 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 File Size: 65KB. Graduate Student Seminar Summer Term Nilpotence in Stable Homotopy Theory We start with a concrete question.

Let X be a finite CW-complex and f: ΣdX → X a map from the d-th suspension of X to X itself. We can iterate this map and get f(k): ΣdkX → X. Question 1. Is there a method to detect whether f is stably nilpotent in. Annals of Mathematics Studies.

出版社: Nilpotence and Periodicity in Stable Homotopy Theory Ravenel, Douglas C. / / $ (目前无人评价) "Nilpotence and Periodicity in Stable Homotopy Theory" describes some major ad Exponential Sums and Differential Equations Katz, Nicholas M.

/ / $ Introduction to stable homotopy theory (Rough notes - Use at your own risk) Lennart Meier Decem File Size: KB.

This book gives an axiomatic presentation of stable homotopy theory. It starts with axioms defining a “stable homotopy category”; using these axioms, one can make various constructions—cellular towers, Bousfield localization, and Brown representability, to name a few. Ravenel, Douglas C. (), Nilpotence and periodicity in stable homotopy theory, Annals of Mathematics Studies,Princeton University Press, ISBNMR ; Further reading.

Connection of X(n) spectra to formal group laws. Nilpotence and Periodicity in Stable Homotopy Theory, volume of Annals of Mathematics Studies. Princeton University Press, Princeton University Press, Google ScholarCited by: 6.

In mathematics, stable homotopy theory is that part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor.A founding result was the Freudenthal suspension theorem, which states that given any pointed space, the homotopy groups + stabilize for sufficiently large.

This book is a compilation of lecture notes that were prepared for the graduate course ``Adams Spectral Sequences and Stable Homotopy Theory'' given at The Fields Institute during the fall of The aim of this volume is to prepare students with a knowledge of elementary algebraic topology to study recent developments in stable homotopy Cited by:   This is the first in a series of papers whose goal is to investigate certain phenomena in equivariant stable homotopy theory revolving around the categorical notion of nilpotence.

Our starting point is the classical theorem of Quillen [63] on the cohomology of a finite group G, which describes H ⁎ (B G ; k) for k a field of characteristic Cited by:   The aim of this volume is to prepare students with a knowledge of elementary algebraic topology to study recent developments in stable homotopy theory, such as the nilpotence and periodicity le as a text for an intermediate course in algebraic topology, this book provides a direct exposition of the basic concepts of bordism 3/5(1).

Ravenel's "Nilpotence and periodicity in stable homotopy theory" Free Download posted by Jason Polak on Wednesday Ma with No comments. and filed under algebraic-topology, books Doug Ravenel has made his book Nilpotence and periodicity in stable homotopy theory available for free download along with a list of errata, also available.

Stable homotopy theory. Pages Adams, J. Frank. Preview. Applications of homological algebra to stable homotopy theory. Pages Adams, J. Frank. Preview. Theorems of periodicity and approximation in homological algebra.

Pages Adams, J. Frank Book Title Stable Homotopy Theory Authors. Adams; Series Title Lecture Notes Brand: Springer-Verlag Berlin Heidelberg. Books J. Adams, Stable Homotopy and Generalised Homology, Univ. of Chicago Press, D. Ravenel, Nilpotence and Periodicity in Stable Homotopy Theory, Ann.

of Math. Stud-iesGenetics of homotopy theory and the Adams conjecture, Ann. of Math. (), Abstract. In the ’s, remarkable advances were made by Ravenel, Hopkins, Devinatz, and Smith toward a global understanding of stable homotopy theory, showing that some major features arise “chromatically” from an interplay of periodic phenomena arranged in a hierarchy (see [20], [21], [28]).Cited by:   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 and Author: Gerd Faltings.

Ravenel's "Nilpotence and periodicity in stable homotopy theory" Free Download posted by Jason Polak on Wednesday Ma with No comments. and filed under algebraic-topology, books.

Doug Ravenel has made his book Nilpotence and periodicity in stable homotopy theory available for free download along with a list of errata, also available at the same page as the book. Abstract We study various applications of the ideas of descent and nilpotence to stable homotopy theory.

In particular, we give a descent-theoretic calculation of the Picard group of topological modular forms and we prove a partial analog of Thomason’s etale descent theorem in the algebraic K-theory Author: Akhil Mathew. Nilpotence and Stable Homotopy Theory II Gabriel Angelini-Knoll 1 In the beginning there were CW complexes Homotopy groups are such a natural thing to think about as algebraic topologists because they tell us about attaching maps of CW-complexes.

If we have a map, iS. Books. Complex Cobordism and Stable Homotopy Groups of Spheres, Academic Press, New York, Nilpotence and Periodicity in Stable Homotopy Theory, Annals of Mathematics Studies, NumberPrinceton, Complex Cobordism and Stable Homotopy Groups of Spheres, Second edition, AMS Chelsea Publishing, Providence, Conference proceedings.

In mathematics, the Bott periodicity theorem describes a periodicity in the homotopy groups of classical groups, discovered by Raoul Bott (, ), which proved to be of foundational significance for much further research, in particular in K-theory of stable complex vector bundles, as well as the stable homotopy groups of periodicity can be formulated in numerous ways, with.

stable homotopy groups of spheres Download stable homotopy groups of spheres or read online books in PDF, EPUB, Tuebl, and Mobi Format. Click Download or Read Online button to get stable homotopy groups of spheres book now. This site is like a library, Use search box in the widget to get ebook that you want.D.C.

Ravenel, "Complex cobordism and stable homotopy groups of spheres", Pure and Applied Mathematics,Acad. Press () [a7] D.C. Ravenel, "Nilpotence and periodicity in stable homotopy theory", Annals of Math.

Stud.,Princeton Univ. Press () [a8].Subscribe. Subscribe to this blog.

26654 views Sunday, November 8, 2020