Topology II
Math 205B - Winter 2017

Instructor: Carl Mautner
Meeting time: MWF 9-10 in room Surge 284.
Office hours: MF 1-2 (or by appointment) in room 255 Surge


Course Description:

  • Seifert-Van Kampen Theorem,
  • Classification of Covering Spaces,
  • Simplicial and chain complexes,
  • Simplicial and singular homology, and applications.
  • More if time permits...
  • Text: For the first part of the class, we will continue where 205A left off using the textbook Topology by Munkres. We will then transition to Algebraic Topology by Allen Hatcher. The latter is available for free online at the author's website as well as in print.

    Grades: The grade will be based on homework assignments (20%), one midterm exam (30%) and a final exam (50%).

    Homework: Homework will generally be assigned over the course of the week and due the following Wednesday. A list of the homework problems will be kept on the webpage.

    Collaboration policy: You are encouraged to discuss homework problems with other students. However, you should think about the problems yourself before discussing them with others and the final write-up of any solution should be your own. Copying other students' solutions is not allowed. For each question on the problem set, please write a list of everyone with whom you collaborated on that problem. If you did not collaborate with anyone, please explicitly write, "No collaborators."

    Homework assignments:
    1) (Due Jan. 18) - The following problems numbers refer to Hatcher's text. To hand in: Section 1.2, problems 4, 8, 9. Please also think about the following extra questions for discussion, but not to hand in: 3, 14. Also to think about but not hand in: Give RP^n a cell complex structure with one cell e^i in each dimension less than or equal to n (if you are stumped, you can read an explanation under Example 0.4 of Hatcher).
    2) (Due Feb. 1) - Section 1.3 in Hatcher: to hand in 9, 14, 15 and just for discussion 7, 12.
    3) (Due Feb. 8) - Section 1.3 in Hatcher: to hand in 18, 20 and just for discussion 12. 21.
    4) (Due Mar. 3) - Section 2.1 in Hatcher: to hand in 5, 8 and just for discussion 9.
    5) (Due Mar. 17) - Section 2.1 in Hatcher: to hand in 16, 17. To do, but I won't collect: Section 2.2 - 12, 28.

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