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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.
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
- No. of pages:
- © Pergamon 1962
- 1st January 1962
- eBook ISBN: