Questions handed in by students on 2015-11-09.

Admin - 

Lecture - 

1) (Is corollary (A) examinable?) Can we go over the proof of that corollary (A) again?  It got very confusing at the end and was quite rushed.  Thank you.

2) Does the homotopy \tilde{F} that comes out of the HLP preserve endpoints if the original homotopy F does?

3) You sometimes write \pi_1(S^1) = \ZZ and sometimes write \pi_1(S^1) \isom \ZZ, which one do we use.

4) Does It matter what {\pm 1} is?  For instance on S^1 we could do reflection or rotation?  For \RR^n, reflection in any plane or rotation in any axis by 180^\circ and still have -1 self invert.

Exercises - 

1) Exercise 6.1, 6.3 and 6.4 of the Assignment...

2) For p \from \tilde{X} \to X cover, how does the Deck group of p and \pi_1(X) - fundamental group correspond to each other.

3) is \pi_1(A \times B) \isom \pi_1(A) \times \pi_1(B) always true? If not is there some restriction such as A, B path-connected we can impose to make it true?

Beyond - 

1) If we have a group \pi_1(X) then does there exist a \pi_2(X), or a \pi_3(X) etc... ?