Math
246B, Algebraic Topology II

Winter
2013

MWF
2:10-3 pm, Surge 284

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