Foldings and retractions of manifolds and their fundamental groups

Abstract

In this paper, we introduce the definition of the folding on the fundamental group. The folding on a wedge sum of some types of manifolds which are determine by their fundamental group are obtained. Some types of conditional foldings restricted on the elements of the fundamental groups are deduced. The effect of retraction of manifolds on the fundamental group is obtained. The folding of variation curvature of manifolds on their fundamental group are presented. Theorems governing these relations are achieved.