Math 246B, Algebraic Topology II

Winter 2013

MWF 2:10-3 pm, Surge 284

Course Information

Monday, January 7: Higher homotopy groups

Wednesday, January 9: No class

Friday, January 11: No class

Monday, January 14: Properties of higher homotopy groups

Wednesday, January 16: Relative homotopy groups

          Homework 1 due (can be found on iLearn)

Friday, January 18: Whitehead’s Theorem

Wednesday, January 23: CW approximation

          Homework 2 due

Friday, January 25: Freudenthal Suspension Theorem

Monday, January 28: Calculations of homotopy groups

Wednesday, January 30: Hurewicz Theorem

Homework 3 due

Friday, February 1: Fibrations

Monday, February 4: Long exact sequence for fibrations

Wednesday, February 6: Comparing fiber bundles and fibrations

          Homework 4 due

Friday, February 8: Fibrations associated to arbitrary maps

Monday, February 11: Path fibrations and loop spaces

Wednesday, February 13: Cofibrations

          Homework 5 due

Friday, February 15: Brown representability

Monday, February 18: No class

Wednesday, February 20: Serre spectral sequence

          Homework 6 due

Friday, February 22: Exact couples

Monday, February 25: Calculations with the Serre spectral sequence

Wednesday, February 27: Proof of Freudenthal Suspension Theorem using the Serre spectral sequence

          Homework 7 due

Friday, March 1: Cohomology of fiber bundles (Jesse)

Monday, March 4: Hopf invariant (Donna)

Wednesday, March 6: Direct and inverse limits (Matthew)

Friday, March 8: Spectra and homology theories (Kaylee)

Monday, March 11: Guest lecture (Stefano Vidussi)

Wednesday, March 13: No class

Friday, March 15: G-actions and spectral sequences (Soheil)

Last updated: 15 March 2013