Read section starting p 128 on equivalence of singular and simplicial homology. Now you know it and may use it.<\/p>\n
Turn in 3 problems from the ones below<\/p>\n
Disclaimer: You should do all of the suggested problems on your own, and I will assume that you do. I would recommend (for the midterm, final, and qualifying exams) that you do many other problems. I am available for help.<\/p>\n
Due Wednesday, April 8.<\/p>\n
Suggested problems:<\/p>\n
Hatcher p 155<\/p>\n
# 3, 4, 8, 9c, 12, 27.<\/p>\n
On 9c, describe geometrically the generators of the homology groups.<\/p>\n
On 8, follow this hint if you wish: first show that \\(\\widehat{f}: S^2 \\to S^2 \\) is homotopic to \\(z^{\\mathrm{deg\\ } f}\\) where \\( f(z):\\mathbb{C}\\to\\mathbb{C} \\) is the polynomial you are given. Then there is only one thing to show on this problem. Why?<\/p>\n
Read Example 2.31 p 136, and Exercise 1 p 155.<\/p>\n
A. Any problem you didn’t do from Homework 9.<\/p>\n","protected":false},"excerpt":{"rendered":"
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