Lecture Notes of the 1997 Summer School:
"FUNDAMENTAL ALGEBRAIC TOPOLOGY"
The following lecture notes are available:
- Clemens Berger:
- Espaces de lacets itérés et
groupes symétriques. PostScript
file.
- Ronnie Brown:
- Groupoids and crossed objects in algebraic
topology. PostScript file.
- Yves Félix:
- Sullivan minimal models. Dvi file.
- Takuji Kashiwabara:
- Homology of infinite loop spaces and
cohomology operations. Dvi and PostScript files.
- Jean-Louis Loday:
- Lionel Schwartz:
- Unstable modules and unstable algebras;
applications to homotopy theory. Dvi
and PostScript files.
- Francis Sergeraert:
- Hans Baues:
- Homotopy types. Not available here: the lecture notes of
Hans Baues' courses was the paper Homotopy Types, pages 1-72
of James' Handbook of Algebraic Topology, North-Holland, 1995.
Contents of these papers
Clemens Berger:
- Espaces de lacets itérés et
groupes symétriques. PostScript
file.
- Reconnaître et reconstruire un espace de lacets
itérés.
- Structure cellulaire des E_n-opérades.
- Homologie du groupe symétrique infini.
Ronnie Brown:
- Groupoids and crossed objects in algebraic
topology. PostScript file.
- Introduction.
- Groupoids in homotopy theory.
- The search for higher order versions of the fundamental group
in homotopy theory.
- Whitehead's work on crossed modules.
- The 2-dimensional Van Kampen theorem.
- Computation with crossed modules and second relative homotopy groups.
- Preliminaries on double groupoids.
- The homotopy double groupoid of a triple of spaces.
- The 2-dimensional Van Kampen theorem.
- The category of crossed complexes.
- Homotopies of morphisms of crossed complexes.
- Relations with chain complexes with operators.
- Cohomology classes.
- Further work.
Yves Félix:
- Sullivan minimal models. Dvi file.
- The first homotopy groups of a 1-connected space.
- The dichotomy theorem.
- Fibrations.
- Adams-Hilton models.
- Spaces of category 2.
Takuji Kashiwabara:
- Homology of infinite loop spaces and
cohomology operations. Dvi and PostScript files.
- Stable and unstable cohomology operations.
- Hoph rings and homology of infinite loop spaces.
- Algebras over unstable operations.
- For further study.
Jean-Louis Loday:
- Introduction.
- Opérades K-linéaires.
- Dualité de Koszul dans les algèbres associatives.
- Dual d'une opérade quadratique.
- Dualité de Koszul des opérades.
- Applications.
Lionel Schwartz:
- Unstable modules and unstable algebras;
applications to homotopy theory. Dvi
and PostScript files.
- The mod 2 Steenrod algebra {\cal A}_2;
unstable modules and unstable algebras.
- Injective objects in {\cal U}; Lannes' T functor.
- Applications of the functor T.
Francis Sergeraert:
- Introduction.
- CW-complexes.
- The category \Delta.
- Simplicial sets.
Francis Sergeraert:
- Introduction.
- Is a spectral sequence an algorithm?
- Functional algorithmic, a survey.
- Objects with effective homology.
- Perturbation lemma machinery.
- Rubio's solution to Adam's problem.
- A program.
Francis Sergeraert
- Introduction.
- General organization.
- Functional programming in Lisp.
- Functional programming and infinite simplicial sets.
- A mathematical definition is not necessarily a constructive definition.
- The EAT program.
- EAT and the loop spaces.
- A tentative appropriate mathematical language.
- The general organization revisited.
- The basic perturbation lemma.
- Bicomplexes and cones.
- Tensor products.
- Fibrations.
- The twisted Eilenberg-Zilber theorem.
- The SERRE_EH algorithm.
Web Page of F. Sergeraert