Non trivial soft first fundamental group

Abstract In this article, we have aimed to construct a non-trivial fundamental group of soft homotopy classes and find out its applications. To achieve this, firstly we have defined soft exponential mappings, a soft lift of a soft continuous mapping, and studied their important behaviors. Moreover, path lifting property, homotopy lifting property, etc., and their relationship in soft set setting are discussed. Finally, we have constructed the fundamental group of soft homotopy classes of unit circle $\mathbb{S}^1.$ 2010 Mathematics Subject Classification: 14H30, 14H99, 20F34.