Due Friday, October 5

3.5.8, 3.5.9, 3.5.11, 3.8.1, 3.8.3

I will select some problems from those to grade. Please ask me about any questions you have on the problems that are not graded.

Due Friday, October 30

3.2.3, 3.3.5 through 3.3.8, From Section 3.11: #11, 12, 22

A. If \(f:(X,x) \to (Y,y)\) is a continuous map of pointed topological spaces, verify that \(f_\ast: \pi_1(X,x) \to \pi_1(Y,y)\) is a group homomorphism. I showed you the steps in class. Justify them.

B. If \(f:(X,x) \to (Y,y)\) and \(g:(Y,y) \to (Z,z)\), verify that \(g_\ast \circ f_\ast = (g\circ f)_\ast\).

C. If \(f:(X,x) \to (X,x)\) is the identity map, prove \(f_\ast\) is the identity map on the fundamental group.

I will select some problems from those to grade. Please ask me about any questions you have on the problems that are not graded.