Lecture Notes of the 1997 Summer School:

"FUNDAMENTAL ALGEBRAIC TOPOLOGY"


The following lecture notes are available:


Contents of these papers


Clemens Berger:

  1. Reconnaître et reconstruire un espace de lacets itérés.
  2. Structure cellulaire des E_n-opérades.
  3. Homologie du groupe symétrique infini.

Ronnie Brown:

  1. Introduction.
  2. Groupoids in homotopy theory.
  3. The search for higher order versions of the fundamental group in homotopy theory.
  4. Whitehead's work on crossed modules.
  5. The 2-dimensional Van Kampen theorem.
  6. Computation with crossed modules and second relative homotopy groups.
  7. Preliminaries on double groupoids.
  8. The homotopy double groupoid of a triple of spaces.
  9. The 2-dimensional Van Kampen theorem.
  10. The category of crossed complexes.
  11. Homotopies of morphisms of crossed complexes.
  12. Relations with chain complexes with operators.
  13. Cohomology classes.
  14. Further work.

Yves Félix:

  1. The first homotopy groups of a 1-connected space.
  2. The dichotomy theorem.
  3. Fibrations.
  4. Adams-Hilton models.
  5. Spaces of category 2.

Takuji Kashiwabara:

  1. Stable and unstable cohomology operations.
  2. Hoph rings and homology of infinite loop spaces.
  3. Algebras over unstable operations.
  4. For further study.

Jean-Louis Loday:

  1. Introduction.
  2. Opérades K-linéaires.
  3. Dualité de Koszul dans les algèbres associatives.
  4. Dual d'une opérade quadratique.
  5. Dualité de Koszul des opérades.
  6. Applications.

Lionel Schwartz:

  1. The mod 2 Steenrod algebra {\cal A}_2; unstable modules and unstable algebras.
  2. Injective objects in {\cal U}; Lannes' T functor.
  3. Applications of the functor T.

Francis Sergeraert:

  1. Introduction.
  2. CW-complexes.
  3. The category \Delta.
  4. Simplicial sets.

Francis Sergeraert:

  1. Introduction.
  2. Is a spectral sequence an algorithm?
  3. Functional algorithmic, a survey.
  4. Objects with effective homology.
  5. Perturbation lemma machinery.
  6. Rubio's solution to Adam's problem.
  7. A program.

Francis Sergeraert

  1. Introduction.
  2. General organization.
  3. Functional programming in Lisp.
  4. Functional programming and infinite simplicial sets.
  5. A mathematical definition is not necessarily a constructive definition.
  6. The EAT program.
  7. EAT and the loop spaces.
  8. A tentative appropriate mathematical language.
  9. The general organization revisited.
  10. The basic perturbation lemma.
  11. Bicomplexes and cones.
  12. Tensor products.
  13. Fibrations.
  14. The twisted Eilenberg-Zilber theorem.
  15. The SERRE_EH algorithm.

Web Page of F. Sergeraert