Complexes and Manifolds

Complexes and Manifolds

The Mathematical Works of J. H. C. Whitehead

1st Edition - January 1, 1962

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  • Editor: I. M. James
  • eBook ISBN: 9781483150291

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The Mathematical Works of J. H. C. Whitehead, Volume 2: Complexes and Manifolds contains papers that are related in some way to the classification problem for manifolds, especially the Poincare conjecture, but towards the end one sees the gradual transition in the direction of algebraic topology. This volume includes all Whitehead's published work up to the year 1941, as well as a few later papers. The book begins with a list of Whitehead's works, in chronological order of writing. This is followed by separate chapters on topics such as analytical complexes; duality and intersection chains in combinatorial analysis situs; three-dimensional manifolds; doubled knots; certain sets of elements in a free group; certain invariants introduced by Reidemeister; and the asphericity of regions in a 3-sphere. Also included are chapters on the homotopy type of manifolds; the incidence matrices, nuclei and homotopy types; vector fields on the n-sphere; and operators in relative homotopy groups.

Table of Contents

  • Editorial Preface

    Publications of J. H. C. Whitehead

    On Analytical Complexes (with S. Lefschetz)

    On Duality and Intersection Chains in Combinatorial Analysis Situs

    On Subdivisions of Complexes

    Certain Theorems about Three-dimensional Manifolds (I)

    Three-Dimensional Manifolds (Corrigendum)

    A Certain Region in Euclidean 3-Space

    A Certain Open Manifold Whose Group is Unity

    On the Group of a Certain Linkage (with M. H. A. Newman)

    On Doubled Knots

    On Certain Sets of Elements in a Free Group

    On Equivalent Sets of Elements in a Free Group

    Simplicial Spaces, Nuclei and m-Groups

    On Certain Invariants Introduced by Reidemeister

    On the Asphericity of Regions in a 3-Sphere

    On C1-Complexes

    On the Homotopy Type of Manifolds

    Note on Manifolds

    On Adding Relations to Homotopy Groups

    Note on a Previous Paper Entitled "On Adding Relations to Homotopy Groups"

    On Incidence Matrices, Nuclei and Homotopy Types

    On the Groups πr(Vn,m ) and Sphere-Bundles

    On the Groups πr(Vn,m) and Sphere-Bundles (Corrigendum)

    Vector Fields on the n-Sphere (with N. E. Steenrod)

    On Operators in Relative Homotopy Groups

    Note on Suspension

    Teoria della Dimensione


    Contents of Volumes I to IV

Product details

  • No. of pages: 450
  • Language: English
  • Copyright: © Pergamon 1962
  • Published: January 1, 1962
  • Imprint: Pergamon
  • eBook ISBN: 9781483150291

About the Editor

I. M. James

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