nLab Handbook of Algebraic Topology


This page collects material and links related to

collecting survey articles on subjects in algebraic topology/homotopy theory.



  • Foreword.

  • List of Contributors.

  1. Homotopy Types (H.-J. Baues).

  2. Homotopy theories and model categories (W.G. Dwyer, J. Spalinski).

  3. Proper Homotopy Theory (T. Porter).

  4. Introduction to fibrewise homotopy theory (I.M. James).

  5. Coherent homotopy over a fixed space (K.A. Hardie, K.H. Kamps).

  6. Modern foundations for stable homotopy theory (A.D. Elmendorf et al.)

  7. Completions in algebra and topology (J.P.C. Greenlees, J.P. May).

  8. Equivariant stable homotopy theory (J.P.C. Greenlees, J.P. May).

  9. The stable homotopy theory of finite complexes (D.C. Ravenel).

  10. The EHP sequence and periodic homotopy (M. Mahowald, R.D. Thompson).

  11. Introduction to nonconnective Im(J)Im(J)-theory (M.C. Crabb, K. Knapp).

  12. Applications of nonconnective Im(J)Im(J)-theory (K. Knapp).

  13. Stable homotopy and iterated loop spaces (G. Carlsson, R.J. Milgram).

  14. Stable operations in generalized cohomology (J. M. Boardman).


  15. Unstable operations in generalized cohomology (J. M. Boardman, D. C. Johnson, W. S. Wilson)


  16. Differential graded algebras in topology (Y. Felix et al.).

  17. Real and rational homotopy theory (Edgar H. Brown, Robert H. Szczarba)

    on real homotopy theory

    and Borel-equivariant rational homotopy theory applied to covering spaces of non-nilpotent spaces


  18. Cohomology of groups (D.J. Benson, P.H. Kropholler).

  19. Homotopy theory of Lie groups (M. Mimura).

  20. Computing v 1v_1-periodic homotopy groups of spheres and some compact Lie groups (D.M. Davis).

  21. Classifying spaces of compact Lie groups and finite loop spaces (D. Notbohm).

  22. H-spaces with finiteness conditions (J.P. Lin).

  23. Co-H-spaces (Martin Arkowitz).

  24. Fibration and product decompositions in nonstable homotopy theory (F.R. Cohen).

  25. Phantom maps (C.A. McGibbon).

  26. Wall’s finiteness obstruction (G. Mislin).

  27. Lusternik-Schnirelmann category (I.M. James).

category: reference

Last revised on September 23, 2021 at 16:04:03. See the history of this page for a list of all contributions to it.