Set 1 for wed

Work out the three problems mentioned in class. Finish the calculation of H₀(X) for a topological space X.

Set 2 for wed

Chapter 0: 1,4,5, 6, 11, 16

Set 3 for wed

2.1: 1, 11, 12, 13, 14

Set 4

2.1: 15,16,17 2.2: 1, 2, 3, 4

Set 5

2.2: 7 Prove that if a smooth f : ℝⁿ → ℝⁿ is non-singular at x₀ then the induced map H_n(ℝⁿ, ℝⁿ − x₀) → H_n(ℝⁿ, ℝⁿ − f(x₀)) is id or −id according to whether Df(x₀) is orientation preserving or reversing.

Set 6

2.2: 20,21,22,23,29

Set 7

3.1: 6,7,9,13