Up: Math 232B: Algebraic Topology

# Homework List for Math 232B Algebraic Topology

Assignment: 1 |2 |3 |4 |5 |6

### Assignment 1

Due Date: Tuesday January 15th
• 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: Thursday January 24th (changed to Tuesday January 29th)
• 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 February 5th
• Read: p.197-204 (Cohomology of spaces)
• Do: Exercises 5,6, and 8 on p.205.

### Assignment 4

Due Date: Thursday February 14th
• Read: p. 206-213 (Cup product)
• Do: Exercises 1,3, and 4 on p.228-9.

### Assignment 5

Due Date: Thursday February 28th
• Read: p. 214-219 (Kunneth Formula)
• Do: Exercises 6,7,9, and 11 on p.229.

### Assignment 6

Due Date: Tuesday March 11th
• Read: p. 230-239 (Orientations and Homology)
• Do: Exercises 3,4,5,7 on p.257-8