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.
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.
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.
Monday, May 8: Hilbert's theorem on syzygies. Section 4.3.
Wednesday, May 10: (Co)homology of groups: definitions.
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.
Wednesday, May 17: The Bar resolution. Section 6.5.
Friday, May 19: Extensions and H^2. Section 6.6.
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.
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.