Algebraic Topology II

Spring 2011


Course Information

Monday, March 28: Review of singular homology

Wednesday, March 30: Computations of homology with coefficients and cohomology

          Homework 1 due Friday, April 1

Friday, April 1: Definition of cup products

Monday, April 4: Digression on degree

Wednesday, April 6: Using degree to understand homology of real projective space

Friday, April 8: Universal coefficient theorem for cohomology

Monday, April 11: Computing cup products

Wednesday, April 13: More computations of cup products

          Homework 2 due Friday, April 15

Friday, April 15: Ring structure for the cohomology of projective spaces

Monday, April 18: More examples of ring structures

Wednesday, April 20: Graded commutativity of cup products

          Homework 3 due Friday, April 22

Friday, April 22: Proof of the universal coefficient theorem for cohomology

Monday, April 25: Universal coefficient theorem for homology

Wednesday, April 27: Cellular chains on product spaces

Homework 4 due Friday, April 29

Friday, April 29: More on cellular chains on products

Monday, May 2: Tensor products of chain complexes

Wednesday, May 4: The Künneth Theorem

          Homework 5 due Friday, May 6

Friday, May 6: Orientation

Monday, May 9: R-orientation

Wednesday, May 11: Poincaré duality

          Homework 6 due Friday, May 13

Friday,  May 13: Cup product pairing

Monday, May 16: Higher homotopy groups

Wednesday, May 18: Eilenberg-Mac Lane spaces and fiber bundles

          Homework 7 due Friday, May 20

Friday, May 20: Brown Representability

Monday, May 23: Edward Burkard – Relationship between de Rham and singular cohomology

Wednesday, May 25: Jacob West – The Dold-Kan correspondence

Friday, May 27: Chris Rogers – Characteristic classes

Monday, May 30: No class – Memorial  Day

Wednesday, June 1: Dennis Gumaer – Geometric uses for homology

Friday, June 3: Matt Highfield – Direct and inverse limits


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Last updated: 1 June 2011