September 9: Class policy, Singular Chains
September 11: The singular chain complex. Categories, functors, natural transformations.
September 21: CW homology and cohomology. The CW structure on a complex projective space..
September 25: The universal coefficient theorem.
September 28: The CW structure of a complex quadric. Adjoint functors. Derived categories..
September 30: Dearived Category of a small category. Derived functors..Left Kan extension.
October 5: Ends and coends. Simplicial sets. The derived category of R-modules I.
October 7: Derived categories.
October 9: :Dearived functors from "resolultions"
October 12: Whitehead theorem for chain complexes, Tor and Ext: :
October 26:Weak equivalences preserve singular homology. Hurewicz Theorem...
October 28:The long exact sequence of homotopy groups..
October 30:Cofibrations and fibrations. Mapping cone. Relative cohomology and cofibrations...
November 2:Fibrations. Examples of homotopy groups of spheres. Simplicial sets...
November 4:Gluing fibrations. Products of simplicial sets and Milnor's theorem..
November 6:The Kan condition. Approximation and co-Whitehead theorem for simplicial sets...
November 11:Eilenberg-Zilber Theorem. Acyclic models.
November 13:Kunneth Theorem. Exact couples and spectral sequences. Kunneth spectral sequence..
November 18:Singular cohomology of a locally contractible space via sheaves..
November 20:Sheaves of simplicial sets. Grothendieck topology. .
November 23:Symmetric monoidal category. Strong duality. .
November 25:Spanier-Whitehead duality..
November 30:Cup product.Alexander duality..
December 2: Poincare duality..
December 4: Comments on Poincare duality and its applications..Vector bundles.
December 7: Comments on vector bundles. Spectra.
December 9: Approximation and Whitehead theorem for May spectra.
December 14: Examples of generalized homology and cohomology theories.