TOPOLOGY

e-mail: laurentiu.maxim@lehman.cuny.edu
office hours: Tue, Thu 1:30-3 PM.

CLASS SCHEDULE: Tue, Thu, 11:45 - 1:15pm, Graduate Center, Room 5417.

CLASS HOMEPAGE: http://comet.lehman.cuny.edu/maxim/MATH70800.html

DESCRIPTION: Fundamental group and Covering spaces; Homology; Cohomology; Poincare Duality.

READING SOURCES:

• Allen Hatcher: Algebraic Topology, available here.
• William Massey: A Basic Course in Algebraic Topology
• James Davis, Paul Kirk: Lecture Notes in Algebraic Topology
• Glen Bredon: Topology and Geometry

MIDTERM EXAM: This is a take-home exam, due on April 7, in class. I expect each of you to work independently on each of the problems.

FINAL EXAM: May 14, 11:45 AM-1:15 PM
There will be an in-class final exam, during our last lecture on May 14.
It is meant to test your knowledge of the following topics: Cohomology and its ring structure, Manifolds and Poincare Duality.
The final exam counts as 50% of your final grade for the course.

GRADE: Midterm: 50%, Final Exam: 50%.

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

• HW 1: Fundamental group.
  
• HW 2: Covering spaces.
  
• HW 3: Singular homology.
  
• HW 4: CW-complexes. Cellular homology.
  
• MIDTERM
  
• HW 5: Cohomology and its ring structure.
  
• HW 6: Manifolds and Poincare Duality.
  
• HW 7: Miscellaneous Problems.