Homotopy Theory

Homotopy Theory

The Mathematical Works of J. H. C. Whitehead

1st Edition - January 1, 1962

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  • Editor: I. M. James
  • eBook ISBN: 9781483184760

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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

Product details

  • No. of pages: 468
  • Language: English
  • Copyright: © Pergamon 1962
  • Published: January 1, 1962
  • Imprint: Pergamon
  • eBook ISBN: 9781483184760

About the Editor

I. M. James

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