Due Date: Tuesday January 15th
Due Date: Thursday January 24th (changed to Tuesday January 29th)
- 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)
Due Date: Tuesday February 5th
- Read: p.190-197 (Universal Coefficient Theorem)
- Do: The exercise on p.193, plus Exercises 1 and 2 on p.204
Due Date: Thursday February 14th
- Read: p.197-204 (Cohomology of spaces)
- Do: Exercises 5,6, and 8 on p.205.
Due Date: Thursday February 28th
- Read: p. 206-213 (Cup product)
- Do: Exercises 1,3, and 4 on p.228-9.
Due Date: Tuesday March 11th
- Read: p. 214-219 (Kunneth Formula)
- Do: Exercises 6,7,9, and 11 on p.229.
- Read: p. 230-239 (Orientations and Homology)
- Do: Exercises 3,4,5,7 on p.257-8