I am fairly new to algebraic topology so please bare with me if this seems simple
I am trying to find the fundamental group of the unit disk with the identification on the boundary z = (cos(θ), sin(θ)) being mapped to (cos(θ+2π/n), sin(θ+2π/n)).
For n=1 it is just the disc so the fundamental group is trivial (since the disk is convex).
Therefore, I was trying to solve it for n=2 to begin. With n=2 each point on the boundary is being identified to its antipodal point.
I was trying figure out a way to use van kampen's theorem.
As I know it, van kampen's theorem states that if X = A∪B (A and B open) and A∩B path-connected, then π1(X) = [π1(A) * π1(B)] / π1(A∩B)
(where * is the free product and you quotient out by the fundamental group of the intersection)
I think that there probably is a way by letting A equal the interior of the disk, but I am not sure what to make B since I am even having trouble seeing what the open sets in the quotient space are.
Thanks for the help