1.      In C  consider the circle centered at (0,0) and of radius 1 intersecting the x-axis at W. Consider the circle centered at (1,0)  and of radius 1 intersecting the first circle at A and B.  Consider the points P(-1,0) and Q(2,0) and let denote the arcs BQA,BWA,APB respectively. 

a)      Give the parametric representation of in and show that is homotopic to in C-{0}.

b)      Show, in two different ways, that .

c)      Show that and are homotopic in C.

d)      Show that .  Does this contradict part 3? .