The Seifert-Van Kampen Theorem

Abstract

In this paper, the Seifert – Van Kampen Theorem deals with the situation where a path-connected space may be written as the union of two open path-connected intersection. The fundamental group of the space is isomorphic to the co-limit of the diagram of the fundamental groups of the three subspaces. We also considered the fact that the fundamental groups are all injective, the fundamental group of the space is a classical free product with amalgamation and also a free product with the amalgamation in the category of rings. Keywords : Fundamental groups, Homotopy, Homomorphism, Seifert-Van Kampen, Simply Connected, Knot Theory.