Homework Problems

1. For 2/5: Show that a Δ-complex is a CW-complex.


2. For 2/5: If X=T#T is the orientable surface of genus 2, exhibit a Δ-complex structure on X, and use it to compute the simplicial homology of X.


3. For 2/5: Problem #5 from §2.1 in Hatcher (page 131)


4. Problems #1, 4, 8, 23 from §2.1 in Hatcher (page 131)


5. (Never mind, you don't have to compute the homology of the Klein bottle twice...)


6. For 2/24: Problems #11 - 13 from §2.1 in Hatcher (page 132)


7. For 3/5: Problems #16, 17, 20 from §2.1 in Hatcher (page 132)


8. For 3/5: Compute the local homology groups H_*(CT,CT-x), where T is the 2-dimensional torus, CT is the cone on T, and x is the cone point.


9. Compute the homology of the configuration space of 3 ordered points in the plane.


10. Problems #29, 30 (the 2nd one), 31 from §2.1 in Hatcher (page 132)
    Problems #1 - 8 from §2.2 in Hatcher (page 155)
    p. 132 #29, p. 155 #2, 5 will be collected Thursday 3/19 (or Tuesday 3/24)


11. Problems #14, 15, 19, 20, 21 from §2.2 in Hatcher (page 156 - 157)
    Compute the cellular homology of the complex projective space CPⁿ
    p. 157 #19, 20 will be collected Thursday 4/16


12. Problems #2, 5, 6, 8, 9 from §3.1 in Hatcher (page 204 - 205)
    p. 205 #6 will be collected Thursday 4/16


13. Problems #1, 3, 7, 18 from §3.2 in Hatcher (page 228 - 230)
    p. 205 #8, p. 229 #3, and possibly others will be collected


14. Find the cohomology ring of the configuration space of 3 ordered points in the plane.


15. Find the cohomology ring of the Klein bottle with Z and Z₂ coefficients.


16. Last homework, due Thursday 5/7:   page 205 #8   and   page 228 #1, 7, 18