MATH 572: ALGEBRAIC TOPOLOGY

Spring 2012

 

Class

week of

Topics

Suggested Problems

1

27/2

Free products of groups. Seifert-van Kampen

1.1: 8, 16, 17. 1.2: 2, 3, 4, 10, 19, 20, 21.

2

5/3

CW complexes. Applications.

0: 2, 6, 14, 16, 19, 20, 23. 1.2: 8, 9, 11, 12, 22.

3

12/3

Covering Spaces. Classification.

1.3: 4, 8, 9, 10, 12.

4

19/3

Deck Transformations. Group Actions.

1.3: 17, 20, 25, 27, 28, 30.

5

26/3

Simplicial and singular homology.

2.1: 5, 8, 12, 15, 17, 22, 29.

6

2/4

Homotopy invariance. Exact sequences. M1

2.2: 1, 4, 7, 12, 14.

7

9/4*

Cellular homology. Mayer-Vietoris sequences.

2.2: 15, 20, 21, 22, 29, 31, 33, 36.

8

16/4

Homology with Coefficients. Hom. & fund. group

2.2: 40, 41.

9

23/4

Classical applications.

2.B: 1, 2, 3, 5, 9, 10, 11.

10

30/4

Cohomology. Universal coefficient theorem.

3.1: 1, 5, 6, 8, 9, 11, 13.

11

7/5

Cup product. Kunneth formula.

3.2: 1, 3, 4, 5, 6, 7, 8, 9, 16, 18.

12

14/5

Orientation. Poincare duality.

3.3: 2, 4, 6, 7, 9, 11, 16, 25.

 

Instructors: Baris Coskunuzer, Tolga Etgu, Burak Ozbagci

Text: A. Hatcher, Algebraic Topology

Midterm 1 Midterm 1 Solutions