Assignment:
1
2
3
4
5
6
Due Date: Tuesday January 15th
 Read: p.185189 three times closely
 Do: Write (in your own words, of course)
a short (12 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 3cube 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 2cell to a circle by a map that wraps around the
circle n times, n at least 2.
 The nsphere, S^{n}
 Complex projective space, CP^{n} (Extra credit)
Due Date: Thursday January 24th (changed to Tuesday January 29th)
 Read: p.190197 (Universal Coefficient Theorem)
 Do: The exercise on p.193, plus Exercises 1 and 2 on p.204
Due Date: Tuesday February 5th
 Read: p.197204 (Cohomology of spaces)
 Do: Exercises 5,6, and 8 on p.205.
Due Date: Thursday February 14th
 Read: p. 206213 (Cup product)
 Do: Exercises 1,3, and 4 on p.2289.
Due Date: Thursday February 28th
 Read: p. 214219 (Kunneth Formula)
 Do: Exercises 6,7,9, and 11 on p.229.
Due Date: Tuesday March 11th
 Read: p. 230239 (Orientations and Homology)
 Do: Exercises 3,4,5,7 on p.2578
