Homework List for Math 232B
Cohomology theory

Assignment 1

• Read: p.185-189 three times closely
• Do: Write (in your own words, of course) a short (1-2 page), complete, concise, thorough description of your calculation of the homology groups for each of the following spaces. Your goal should be to convince me that you have absorbed and retained the major parts of the previous course. Be sure to name and highlight all of the key facts you are using along the way.
  • Start with a solid 3-cube centered at the origin and remove the union of the three coordinate axes.
  • The universal cover of the space obtained by attaching the boundary of a 2-cell to a circle by a map that wraps around the circle n times, n at least 2.
  • The n-sphere, Sⁿ
  • Complex projective space, CPⁿ (Extra credit)

  Assignment 2

  Due Date: Tuesday January 24th
  • Read: p.190-197 (Universal Coefficient Theorem)
  • Do: The exercise on p.193, plus Exercises 1 and 2 on p.204

  Assignment 3

  Due Date: Tuesday January 31st
  • Read: p.197-204 (Cohomology of spaces)
  • Do: Exercises 5,6, and 8 on p.205.

  Assignment 4

  Due Date: Tuesday February 7th
  • Read: p. 206-213 (Cup product)
  • Do: Exercises 1,3, and 4 on p.228-9.

  Assignment 5

  Due Date: Thursday February 23rd
  • Read: p. 214-219 (Kunneth Formula)
  • Do: Exercises 6,7,9, and 11 on p.229.
    

  Assignment 6

  Due Date: Thursday March 8th
  • Read: p. 230-239 (Orientations and Homology)
  • Do: Exercises 3,4,5,7 on p.257-258
  
  That was the last homework assignment