Math 8301: Manifold and Topology
Time
3:35pm - 4:25 pm MWF
Location
Vincent Hall 20
Office
Vincent Hall 365
Zoom Meeting ID
Office hours
1pm-2pm in office on Monday and Friday or by appointment
Textbooks
I will loosely follow
Contents
Classification of compact surfaces, fundamental group/covering spaces. Homology group, basic cohomology. Application to degree of a map, invariance of domain/dimension.
A detailed day by day plan can be found on Canvas.
Prerequisites
Some point-set topology and abstract algebra. In particular, you should be comfortable with connectedness, compactness, Hausdorfness, (co)kernels of linear maps, as well as groups, rings and linear algebra.
Homework
Homework will be assigned on weekly on Canvas. Collaboration on homework is encouraged.
Exams
There are one midterm exam and one final exam. Both exams are take home exams. No collaboration is allowed. You can use books or notes, but you are not allowed to use internet for the exams.
Midterm exam: Exam time: Oct 6 - Oct 10 (4 days)
Final exam: Exam time: Dec 16 - Dec 20 (4 days)
Grading policy
Your grade is based on homework(60%) and the exams(40%).