Homotopy Theory - 1st Edition - ISBN: 9780080098715, 9781483184760

Homotopy Theory

1st Edition

The Mathematical Works of J. H. C. Whitehead

Editors: I. M. James
eBook ISBN: 9781483184760
Imprint: Pergamon
Published Date: 1st January 1962
Page Count: 468
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Homotopy Theory contains all the published mathematical work of J. H. C. Whitehead, written between 1947 and 1955. This volume considers the study of simple homotopy types, particularly the realization of problem for homotopy types. It describes Whitehead's version of homotopy theory in terms of CW-complexes.

This book is composed of 21 chapters and begins with an overview of a theorem to Borsuk and the homotopy type of ANR. The subsequent chapters deal with four-dimensional polyhedral, the homotopy type of a special kind of polyhedron, and the combinatorial homotopy I and II. These topics are followed by reviews of other homotopy types, such as group extensions with homotopy operators, cohomology systems, secondary boundary operator, algebraic homotopy, and the G-dual of a semi-exact couple. The last chapters examine the connected complex homotopy types and the second non-vanishing homotopy groups.

This book will be of great value to mathematicians.

Table of Contents

Editorial Preface

Publications of J. H. C. Whitehead

Note on a Theorem Due to Borsuk

On the Homotopy Type of ANR’s

On Simply Connected, 4-Dimensional Polyhedra (Abstract)

On Simply Connected, 4-Dimensional Polyhedra

The Homotopy Type of a Special Kind of Polyhedron

Combinatorial Homotopy I

Combinatorial Homotopy II

Simple Homotopy Types

On the Realizability of Homotopy Groups

On Group Extensions with Operators

On the 3-Type of a Complex

Note on Cohomology Systems

The Secondary Boundary Operator

Algebraic Homotopy Theory

A Certain Exact Sequence

On the Theory of Obstructions

The G-Dual of a Semi-Exact Couple

On the (n+2)-Type of an (n—1)-Connected Complex (n≥4)

On the Exact Couple of a CW-Triad

On The Second Non-Vanishing Homotopy Groups of Pairs and Triads

The First Non-Vanishing Group of an (n+1)-Ad

Contents of Volumes I to IV


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About the Editor

I. M. James

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