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Betti numbers, Torsion Coefficients and the rise of HomologyEdit

Riemann and BettiEdit

  • Definition of (n+1)-fold connectedness: This definition is correct but somewhat subtle in its logic. "Maximal" is really meant in the sense of posets, even if it first appears that it doesn't. Note that it reads *any subset of C* and NOT *any proper subset of C*.

Poincare and Analysis SitusEdit

Homology of topological spaces (1900-1935).Edit

The rise of algebraic methods (1935-1945).Edit

Homology and cohomology of algebraic systemsEdit

Ext of abelian groupsEdit

Cohomology of GroupsEdit

Associative algebrasEdit

Lie algebrasEdit

Sheaves and Spectral SequencesEdit

The Cartan-Eilenberg RevolutionEdit

Chain ComplexesEdit

Free and Injective resolutionsEdit

Cartan and Eilenberg: the bookEdit

Abelian CategoriesEdit

After the Cartan-Eilenberg RevolutionEdit

Projective ModulesEdit

Homological Algebra and ring theoryEdit

Cohomology Theories in Algebraic GeometryEdit

Derived CategoriesEdit

Simplicial MethodsEdit