Read section starting p 128 on equivalence of singular and simplicial homology. Now you know it and may use it.

Turn in 3 problems from the ones below

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.

Due Wednesday, April 8.

Suggested problems:

Hatcher p 155

# 3, 4, 8, 9c, 12, 27.

On 9c, describe geometrically the generators of the homology groups.

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?

Read Example 2.31 p 136, and Exercise 1 p 155.

A. Any problem you didn’t do from Homework 9.