INTRODUCTORY TOPOLOGY II.

office: 713 Van Vleck
e-mail: maxim@math.wisc.edu
office hours: Monday 1:00-3:00PM

CLASS SCHEDULE: MWF 12:05-12:55PM, Room VAN VLECK B131.

CLASS HOMEPAGE: http://www.math.wisc.edu/~maxim/752s13.html

DESCRIPTION:

Homology: cellular homology, Lefschetz fixed point theorem, universal coefficient theorem.
Cohomology: cohomology groups, cup product, Kunneth formula, 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%).

EXAMS:

The midterm will be in class (50 minutes), on March 15. The final exam will be a take-home.

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

• HW 1: Euler characteristic. Homology with coefficients. (due Feb 8)
  
• HW 2: Basics of Cohomology. (due Feb 25)
  
• HW 3: Cup Products. (due March 8)
  
• HW 4: Kunneth formula. (due March 15)
  
• HW 5: Orientations on manifolds. (due April 5)
  
• HW 6: Poincare Duality. (due April 17)
  
• HW 7: Homotopy Theory. (due May 10)
  

LECTURE NOTES: I intend to post lecture notes at the end of each week of classes.

• Math 752 Lecture notes (updated weekly)