Adams Memorial Symposium on Algebraic Topology : Manchester 1990. 2 / edited by N. Ray and G. Walker. [electronic resource]

Format:

Book

Conference/Event

Contributor:

Ray, Nigel, 1945- editor.

Walker, G. (Grant), editor.

Conference Name:

Adams Memorial Symposium on Algebraic Topology (1990 : Manchester, England)

Series:

London Mathematical Society lecture note series ; 176.

London Mathematical Society lecture note series ; 176

Language:

English

Subjects (All):

Algebraic topology--Congresses.

Algebraic topology.

Physical Description:

1 online resource (xxiii, 305 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 1992.

Language Note:

English

Summary:

J. Frank Adams had a profound influence on algebraic topology, and his works continue to shape its development. The International Symposium on Algebraic Topology held in Manchester during July 1990 was dedicated to his memory, and virtually all of the world's leading experts took part. This two volume work constitutes the proceedings of the symposium; the articles contained here range from overviews to reports of work still in progress, as well as a survey and complete bibliography of Adams' own work. These proceedings form an important compendium of current research in algebraic topology, and one that demonstrates the depth of Adams' many contributions to the subject. This second volume is oriented towards stable homotopy theory, the Steenrod algebra and the Adams spectral sequence. In the first volume the theme is mainly unstable homotopy theory, homological and categorical algebra.

Contents:

Cover; Title; Copyright; Contents; Preface; 1 Progress report on the telescope conjecture; 1 Background; 2 Miller's proof for n = 1 and p > 2; 3 Difficulties for n = 2; 4 Computing the differentials ^(^,1); 5 A parametrized Adams spectral sequence; 6 Disproving the Telescope Conjecture; References; 2 On K*-local stable homotopy theory; 1 Introduction; 2 The classification of KO-module spectra; 3 The classification of AVlocal spectra; References; 3 Detruncating Morava K-theory; 1 Introduction; 2 The Hopf ring for E(n); 3 Lifting Results; 4 Concluding remarks; References

4 On the p-adic interpolation of stable homotopy groups1 Philosophy; 2 Picard groups; 3 Applications; 3.1 The generating hypothesis; 3,2 Interpolation of homotopy groups; References; 5. Some remarks on v1 -periodic homotopy groups; 1 A definition and some examples; 2 Proofs related to the definition; 3 Proofs related to the examples; References; 6. The unstable Novikov spectral sequence for Sp(n), and the power series sinh-1(x); 1 Statement of results; 2 Proofs of Theorems 1.1 and 1.2; 3 The 1-line for Sp(n); 4 Power series; References; 7. Unstable Adams spectral sequence charts; References.

8. On a certain localization of the stable homotopy of the space Xr1. Introduction.; 2. A localization of π(BT2).; 3. Reduction mod pr'.; 4. A localization of the space X Г.; References; 9. Cooperations in elliptic homology; Introducation; 1 Generalities on hopf algeroids of cooperations; 2. K-theory and KO[1/2]-theory; 3. Elliptic homology; Appendix. the elliptic exponential series; References; 10 Completions of G-spectra at ideals of the Burnside ring; 0. General definitions of localizations and completions.; 1. A cohomological construction of completions at / .

2. The general construction of completions at /.3. Statements of results about the homotopy groups of completionsat /; 4. The Segal conjecture and the Atiyah-Segal completion theorem.; 5. Algebraic definitions and topological proofs.; 6. Algebraic proofs.; Appendix: localizations of G-spectra; Bibliography; 11 Theorems of Poisson, Euler and Bernouilli on the Adams spectral sequence; Introduction; 1. Testing the Poisson hypothesis; 2. The Euler characteristic; 3. Applications; References; Author's address; 12 Algebras over the Steenrod algebra and finite H-spaces; Reference

13 The boundedness conjecture for the action of the Steenrod algebra on polynomials1 Introduction; 2 The block notation; 3 The boundedness conjecture; References; 14 Representations of the homology of BV and the Steenrod algebra I; 1. Introduction; 2. The rings M(k) and L(k); 3. The proof of Theorem 2.11; 4. The action of GL(V) on Ln and Mn; References; 15 Generic representation theory and Lannes' T-functor; 1. Introduction; 2. Generic representation theory; 3. Generic representation theory and q; 4. The four properties of Tv; 5. New relationships between Properties A, B. and C

6. Doubling and Property D

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references.

ISBN:

1-139-88474-3

1-107-36668-2

1-107-37136-8

1-107-36177-X

1-107-37011-6

1-299-40443-X

1-107-36422-1

0-511-52631-8