Math 141 - Differential topology

Instructor: Allen Knutson, allenk@math.berkeley.edu
Lectures: MWF 1-2, Room 87 Evans Hall
Course Control Number: 55005
Office: 1033 Evans Hall, 642-4319

Office Hours: Tuesday/Wednesday 2 PM-3 PM, or by appointment (email me)
Prerequisites: Confidence in linear algebra, multivariable calculus
Text: Guillemin and Pollack, "Differential Topology"
Grading: homework (35%), one midterm (20%) and a final exam (35%). The extra 10% will go wherever it does the most good.

The final is Saturday May 19th, 12:30-3:30, in 60 Evans.
Open book, open notes, cumulative through section 4.5 (except 4.4, integration).

Homework: weekly, assigned and due Fridays
TA: James Kelley, kelley@math.berkeley.edu
Here's a survey for you to fill out and bring to class, so I can get an idea of the general background.
Homework #1 is supposedly due Friday 1/26; if you don't have the book yet I'm happy to take it Monday 1/29. The questions (as copied from the book) are here.

Homework #2 due Friday 2/2 (answers in PDF or PostScript)

  • p7 #18
  • p12 #8
  • p18 #3,4
  • Exhibit the Mobius strip as a submanifold of R^3. (Warning: you can't make it as a closed subset.)
    • Homework #3 due Friday 2/9 (answers in PDF or PostScript)
  • p25 #1,2,5,8,9
  • If G is a subgroup of GL_n(R) (which is the group of nxn invertible real matrices), and around some point g the set G can be given a chart, show G is a manifold. [This was the "Lie groups" question]
    • Homework #4 due Friday 2/16 (answers in PDF or PostScript)
  • Let f:X->A be a submersion, g:Y->A just be smooth. Show the fiber product X x_A Y is smooth, and its projection to Y is a submersion.
  • p32 #2,3,6,8
    • Homework #5 due Friday 2/23 (answers in PDF or PostScript)
  • p33 #9
  • p37 #1,2,4,9
    • Homework #6 due Friday 3/2 (answers in PDF or PostScript)
  • p45 #2,3,6,8
    • Homework #7 due Friday 3/16 (answers in PDF or PostScript)
  • p62 #3,5,6,9
    • Homework #8 (answers in PDF or PostScript) Homework #9 (answers in PDF or PostScript) Homework #10 (answers in PDF or PostScript)