One can use van Kampen’s theorem to calculate fundamental groups for topological spaces that can be decomposed into simpler spaces. Thus we can see that there is a commutative diagram including A∩B into A and B and then another inclusion from A&B into s2 and that there is a corresponding diagram of homomorphism b/w the fundamental groups of each subspace. It is clear from this that the fundamental group of s2 is trivial
