INTRODUCTORY TOPOLOGY II.

office: 713 Van Vleck
e-mail: maxim@math.wisc.edu
office hours: Monday 1:00-4:45pm (but I'll answer your questions on any given day if I am around).

CLASS SCHEDULE: MWF 11:00-11:50 am, Room VAN VLECK B131.

CLASS HOMEPAGE: http://www.math.wisc.edu/~maxim/752s12.html

DESCRIPTION:

Cellular homology (review).
Cohomology: cohomology groups, cup product, Poincare duality.
Elements of homotopy theory: higher homotopy groups, methods of calculation.

TEXTBOOK:

• Allen Hatcher: Algebraic Topology, available here.

GRADE:

Based on homework and class participation (25%), a midterm exam (25%) and a final exam (50%).
As part of class participation, each student is expected to type up a week worth of lecture notes.

EXAMS:

The midterm will be in class (50 minutes), on March 16. The final exam will most likely be a take-home.

HOMEWORK: it will be assigned regularly and will be the main source of problems appearing in the exams.

• HW 1: Degrees. CW complexes. Cellular homology. (due 2/10)
  
• HW 2: Euler characteristic. Homology with coefficients. (due 2/20)
  
• HW 3: Basics of cohomology. (due 3/2)
  
• HW 4: Cup products. (due 3/12)
  
• HW 5: Orientability of manifolds. (due 3/30)
  
• HW 6: Applications of Poincare Duality. (due 4/20)
  
• Takehome Final Exam. (due 5/14 in Tommy Wong's maiblox)