nLab Algebraic Homotopy

The book

• Hans Baues,

  Algebraic Homotopy,

  Cambridge studies in advanced mathematics 15,

  Cambridge University Press, (1989)

  doi:10.1017/CBO9780511662522

gives an account of the author’s interpretation of Henry Whitehead‘s Algebraic Homotopy Theory as described in his ICM talk (1950) and his famous papers, Combinatorial homotopy I, (1949), and Combinatorial homotopy II, again (1949). Although the material contained in the first of these papers became central to the development of homotopy theory (CW complexes etc.) soon after its publication, the second paper, treating harder ideas including those of crossed complexes, was relatively ‘unstudied’ until much more recently. This book gives one interpretation of the ideas it developed from a modern point of view. That development continued in Combinatorial Homotopy and 4-Dimensional Complexes.

Preface

Introduction

I Axioms for homotopy theory and examples of cofibration categories

II Homotopy theory in a cofibration category

III The homotopy spectral sequences in a cofibration category

IV Extensions, coverings and cohomology groups of a category

V Maps between mapping cones

VI Homotopy theory of CW-complexes

VII Homotopy theory of complexes in a cofibration category

VIII Homotopy theory of Postnikov towers and the Sullivan-de Rham equivalence of rational homotopy categories

IX Homotopy theory of reduced complexes

Bibliography

Index

References

See also:

• Tim Porter, Review of “Algebraic Homotopy’‘ by H.J.Baues, in Bull. London Math. Soc. 22 (1990) 196-197.

category: reference