Math 282 SPRING 2006, List of lectures

  • On this page I will post content of all lectures with reference to the book. All handouts also will be posted here.
  • Monday, April 3: Preview: extensions and deformations.
  • Wednesday, April 5: More on deformations; complexes. Section 1.1.
  • Friday, April 7: Operations with complexes. Section 1.2. Here is homework!
  • Monday, April 10: Long exact sequence. Homotopies. Sections 1.3-1.4.
  • Wednesday, April 12: Cone and Cylinder. Section 1.5.
  • Friday, April 14: Abelian categories. Left and right exact functors. Section 1.6. New homework!
  • Monday, April 17: Definition of derived functor. Projective resolutions. Sections 2.1-2.2.
  • Wednesday, April 19: Comparison Theorem for projective resolutions. Injective resolutions. Sections 2.2-2.3.
  • Friday, April 21: Existence of derived functors. Sections 2.4-2.5. New homework!
  • Monday, April 24: Balancing Tor and Ext. Section 2.7.
  • Wednesday, April 26: Computing Tor and Ext. Sections 3.1-3.3.
  • Friday, April 28: Ext and extensions. Section 3.4. New homework!
  • Monday, May 1: Universal coefficients Theorem(s). Section 3.6.
  • Wednesday, May 3: Dimensions. Sections 4.1-4.2.
  • Friday, May 5: Global dimension and Tor-dimension. Sections 4.1-4.2. New homework!
  • Monday, May 8: Hilbert's theorem on syzygies. Section 4.3.
  • Wednesday, May 10: (Co)homology of groups: definitions. Section 6.1.
  • Friday, May 12: Computations of group cohomology for cyclic and free groups. Section 6.2.
  • Monday, May 15: Shapiro's Lemma; crossed homomorphisms and H^1. Sections 6.3-6.4.
  • Wednesday, May 17: The Bar resolution. Section 6.5.
  • Friday, May 19: Extensions and H^2. Section 6.6. New homework!
  • Monday, May 22: Schur-Zassenhaus Theorem. Restriction and corestriction. Sections 6.6-6.7.
  • Wednesday, May 24: Transfer maps, cup products. Section 6.7.
  • Friday, May 26: Lyndon-Hochschild-Serre spectral sequence. Section 6.8.
  • Wednesday, May 31: Exact couples. Section 5.9.
  • Friday, June 2: Overview of Lie algebra (co)homology. Chapter 7.
  • Monday, June 5: Overview of Hochschild (co)homology. Chapter 9.
  • Wednesday, June 7: The derived category. Chapter 10.
  • Friday, June 9: An example of derived equivalence: Koszul duality for symmetric/exterior algebra.
  • THE END.