Indian Journal of Science and Technology

Abstract

The purpose of this paper is to give a combinatorial characterization and also construct representations of the chaotic fundamental groups of the chaotic submanifolds of chaotic Buchdahi space by using some geometrical transformations. The chaotic homotopy groups of the limit for chaotic Buchdahi space are presented. The chaotic fundamental groups of some types of chaotic geodesics in chaotic Buchdahi space are discussed. New types of homotopy maps are deduced. 1. Introduction and Definitions Buchdahi space represents one of the most intriguing and emblematic discoveries in the history of geometry. Although if it were introduced for a purely geometrical purpose, they came into prominence in many branches of mathematics and physics. This association with applied science and geometry generated synergistic effect: applied science gave relevance to Buchdahi space and Buchdahi space allowed formalizing practical problems [6, 8, 21]. In vector spaces and linear maps; topological spaces and continuous maps; groups and homomorphisms together with the distinguished family of maps is referred to as a category. An operator which assigns to every object in one category a corresponding object in another category and to every map in the first a map in the second in such a way that compositions are preserved and the identity map is taken to the identity map is called a functor. Thus, we may summarize our activities thus far by saying that we have constructed a * Corresponding author: A. E. El-Ahmady ([email protected]) Indian Journal of Science and Technology
Keywords: Chaotic Buchdahi Space, Chaotic Homotopy Groups, Chaotic Folding, Chaotic Retractions, Chaotic Deformation Retracts