Algebraic Topology II

Spring 2011

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

Back to Julie Bergner’s Teaching Page

Last updated: 1 June 2011