FREE PRODUCTS OF GROUPS AND FREE GROUPS

Abstract

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.