Soft Topological Folding on the Product of Soft Manifolds and Its Soft Fundamental Group

Abstract

In this study, we analyze the practical applications of soft retraction and soft folding theory on the product of soft manifolds and highlight the role of the soft fundamental group. We propose some novel ideas on the theory of soft manifolds, specifically soft topological folding and soft retraction. We also consider soft topological folding on a finite product of soft manifolds to obtain a new functor on the soft fundamental group. Furthermore, we introduce soft topological folding on the wedge sum of soft manifolds and their induced topological folding on a free product of the soft fundamental group. Based on this framework, we obtain the relationship between a sequence of soft retraction and a sequence of soft topological folding on an n-dimensional soft manifold. Our proposed approach provides some notable insights into the relation between soft folding techniques and topological analysis, as well as the computation of the soft fundamental group.