Adams Memorial Symposium on Algebraic Topology : Manchester 1990. Volume 1 / edited by N. Ray and G. Walker. [electronic resource]

Format:

Book

Conference/Event

Contributor:

Ray, Nigel, 1945- editor.

Walker, G. (Grant), editor.

Adams, J. Frank (John Frank), honoree.

Conference Name:

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

Series:

London Mathematical Society lecture note series ; 175.

London Mathematical Society lecture note series ; 175

Language:

English

Subjects (All):

Algebraic topology--Congresses.

Algebraic topology.

Physical Description:

1 online resource (xxiii, 292 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. Here in the first volume the theme is mainly unstable homotopy theory, homological and categorical algebra. The second volume is oriented towards stable homotopy theory, the Steenrod algebra and the Adams spectral sequence.

Contents:

Cover; Title; Copyright; Contents of Volume 1; Preface; 1 The work of J. F. Adarns; A. The cobar construction, the Adams spectral sequence, higher order cohomology operations, and the Hopf invariant one problem; B. Applications of K-theory; C. Characteristic classes and calculations in K-theory and cobordism; D. Stable homotopy and generalized homology; E. Lectures on Lie groups (1969) [38]; F. Finite H-spaces and compact Lie groups; G. Maps between classifying spaces of compact Lie groups; H. Modules over the Steenrod algebra and their Ext groups

I. Miscellaneous papers in homotopy and cohomology theory. Infinite loop spaces(1975 IAS lecture notes) [61]; K. Two unpublished expository papers; Bibliography of J. F. Adams; 2 Twisted tensor products of DGA's and the Adams-Hilton model for the total space of a fibration; 1. Introduction; 2. Algebraic Preliminaries; 3. Models for twisted tensor products of DGA's; 4. An examination of Brown's equivalence; 5. The Adams-Hilton model for the total space of a fibration; References.; 3 Hochschild homology, cyclic homology, and the cobar construction; Introduction.

5 A splitting result for the second homology group of the general linear group1. Introduction; 2. The second Postnikov section of a double loop space; 3. The naturality of the splitting; References; 6 Low dimensional spinor representations, Adams maps and geometric dimension; 1. Introduction.; 2. Spinor representations.; 3. Proof of Theorems 1, 2 and 3.; 4. An illustrative example.; 5. Constructing the KO-periodic map; References; 7 The characteristic classes for the exceptional Lie groups; 0. Introduction.; 1. The Hopf algebra structure.

2. The Borel theorem and the Eilenberg-Moore spectral sequence.3. The invariant subalgebra of the Weyl group.; 4. The twisted tensor product and the E2-term CotorA{Z/p, Z/p) with A = H*(G; Z/p).; 5. A Z/2-resolution over H*(E8; Z/2).; 6. A Z/3-resolution over H*(Ad E6; Z/3).; References; 8 How can you tell two spaces apart when they have the same n-type for all n?; Example A; Example B; References; 9 A generalized Grothendieck spectral sequence; 1 Introduction; 1.1 Notation; 1.2 Organization; 2 Universal algebras & homotopical algebra; 2.1 universal algebras; 2.1.1 Cuga's

2.1.2 Free algebras and underlying sets

Notes:

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

Includes bibliographical references.

ISBN:

1-139-88473-5

1-107-36667-4

1-107-37135-X

1-107-36176-1

1-107-36950-9

1-299-40442-1

1-107-36421-3

0-511-52630-X