Fall 2005-06
Ma 151a Algebraic and Differential Topology
MWF 10:00  // 153 Sloan
 Daniel Groves

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Note: No Lecture Friday, November 4. Also, no office hours Thursday, November 3.

Course Description: 

Math 151 is the year-long graduate sequence in topology and geometry. In the first term, we'll cover the fundamental group, homology, and some basics of manifold topology. Mostly, the material will closely follow Chapters 0-2 of

Allen Hatcher, Algebraic Topology, Cambridge University Press, 2002.

(This is the required text.)

The full text of this may be downloaded here, but you will probably want to buy it; it is only $32 for over 500 pages. (You may want to look at a useful list of errata.)

Prerequisites are flexible, due to the different background of students. However, you should have an understanding of the basics of point-set topology. The fundamental group will also be covered quickly at the start, and those not familar with this should at least look at Section 1.1 of Hatcher before classes start.

Grading Policy:

There will be weekly homework assignments (50%), a midterm (20%) and a final (30%). Letter grades will be given, unless you specifically enroll otherwise.

Weekly homework is due in class on Fridays at the beginning of class (with beginning slightly generously interpreted -- 10 minutes). Homework turned in after that until the beginning of class on Monday will be graded but count for half-credit. Beyond this, late homework will not be accepted unless an extension is granted before the due date . The lowest homework grade will be dropped. If you will not be in class on Friday, homework may be dropped in the 151a box outside the math department office before the start of class. (Late homework can also be put there). There will be no homework due the week of Thanksgiving (Nov. 24) but there will be lectures on Monday and Wedensday of that week.

Collaboration on homework is encouraged, but all answers must be written up individually, and collaboration must be acknowledged. There is no collaboration allowed on the midterm or final.

The midterm will replace the 6th homework set, and thus be due on Friday, November 4th. It will be given out in class on Friday, October 28th and, beyond that, there are no time restrictions.

The final will be given out in class on Wednesday, November 30th and due at 5pm on Wednesday, December 7th. Once again, otherwise there are no time restrictions for the final.

Homework Assignments

All problem numbers refer to Hatcher's book.

  • HW #1. Due Friday Sept 30.
    • Ch. 0, pg.18: #3,
    • Section 1.1, pg. 38: #2, #3, #6.
  • HW #2. Due Friday Oct. 7.
    • Section 1.1, pp.38-39: #7, #10.
    • Section 1.3, pp.79-80: #6, #7, #9, #15.
  • HW #3. Due Friday Oct. 14.
    • Ch. 0, p.19: #16, #17.
    • Section 1.3, pp.79--80: #10, #12.
    • Section 1.A, p. 87: #9.
  • HW#4. Due Friday Oct. 21.
    • Ch. 0, p.19: #21.
    • Section 1.2, pp.53--54: #9, #14.
    • Section 1.3, pp.80--81: #14, #20,#21.
  • HW#5. Due Friday Oct 28.
    • Section 1.3: #23.
    • Section 2.1: #1, #5, #8, #10(a).
  • HW#6. Due Friday Nov 11.
    • Section 2.1: #12, #15, #17, #22, #29.
  • HW#7. Due Friday Nov 18.
    • Section 2.2: #2, #4, #8, #11, #13.