Folding on the Cartesian product of manifolds and their fundamental groups

Abstract

In this paper we introduce the fundamental group of foldings of the Cartesian product of manifolds into itself. Also the fundamental group of the limit of foldings of the Cartesian product of manifolds into itself are deduced. The effect of folding on the wedge sum of manifolds and their fundamental group will be achieved. Some types of conditional foldings restricted on the elements of a free group and their fundamental groups are presented. Theorems governing these relations are obtained.