Here are some of the things that we have been talking about in our meetings and some questions posed.
1.) Start with a circle. For each point λ on the circumference of the circle, identify λ to -λ . You can not envision the resulting shape but can you find a non-contractible loop? What would the characteristics of the multiplication table of the fundamental group be?
2.) Set G=R and H=Z. What is G/H?
