INTRODUCTORY TOPOLOGY II.

office: 713 Van Vleck
e-mail: maxim@math.wisc.edu
office hours: Mo, 1-3 PM, or by appointment.

CLASS SCHEDULE: MWF 9:55 -10:45, Room VAN VLECK B119.

CLASS HOMEPAGE: http://www.math.wisc.edu/~maxim/MATH752.html

DESCRIPTION: 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: Midterm: 40%, Final Exam: 60%.

EXAMS: The midterm will be in class (50 minutes), on March 10. 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: Basics of cohomology (due Feb. 8)
  
• HW 2: Cup Products (due Feb. 22)
  
• HW 3: Cup Products and Kunneth formula (due March 1)
  
• HW 4: Orientability of manifolds (due March 17)
  
• HW 5: Applications of Poincare Duality (due March 26)
  
• HW 6: Homotopy theory: Whitehead theorem, cellular approximation. (due April 21)
  
• HW 7: Homotopy theory: Hurewicz theorem, fibrations. (due May 7, in class)
  
  Note: This last homework counts as a takehome final exam, so it also contains some problems on cohomology.