Math 205C, Topology

Dr. Julie Bergner

MWF 9:10-10 am, Surge 172

Course Information

Monday, March 29: The covering homotopy theorem

Wednesday, March 31: Corollaries of the covering homotopy theorem

Friday, April 2: The fundamental group of the circle, the Brouwer fixed point theorem, and the lifting theorem

Monday, April 5: More results on covering spaces, and the action of the fundamental group on the fiber

Wednesday, April 7: Deck transformations

Homework 1 due (See iLearn for the problems)

Friday, April 9: Regular covering spaces

Monday, April 12: Covering spaces of orbit spaces

Wednesday, April 14: Classification of covering spaces

Homework 2 due

Friday, April 16: Construction of universal covers

Monday, April 19: The Seifert-Van Kampen Theorem

Wednesday, April 21: CW complexes and calculations using Seifert-Van Kampen

Homework 3 due

Friday, April 23: Spaces with a given fundamental group and the proof of Seifert-Van Kampen

Monday, April 26: End of the proof of Seifert-Van Kampen, and review

Wednesday, April 28: Midterm Exam, and Homework 4 due

Friday, April 30: Euler characteristic

Monday, May 3: Homology of 2-complexes

Wednesday, May 5: Definition of singular homology

Homework 5 due

Friday, May 7: Functoriality of singular homology

Monday, May 10: Relative homology groups and the long exact sequence

Wednesday, May 12: Homotopy invariance

Homework 6 due

Friday, May 14: Excision

Monday, May 17: Class at 8:10 am in Surge 171 and at 9:10 as usual

            Proof of excision for singular homology

Wednesday, May 19: Class at 8:10 am in Surge 171 and at 9:10 as usual

            Results following from excision

            Homework 7 due

Friday, May 21: No class

Monday, May 24: No class

Wednesday, May 26: Class at 9:10 as usual

            Degree

Friday, May 28: No class

Monday, May 31: Memorial Day holiday

Wednesday, June 2: Class at 9:10 as usual

            Computations and cellular homology

            Homework 8 due

Friday, June 4: Class at 8:10 am in Surge 171 and at 9:10 as usual


Last updated: 2 June 2010