Sub-Riemannian-Driven Topological Restructuring of the Alpha Group Induced by the Angular Matrix M(θ)
This work investigates a mechanism for topology-altering geometric behavior induced by angular group actions within the framework of the Alpha Group, demonstrating that a systematic angular sweep can drive spontaneous transitions between Riemannian-like and sub-Riemannian regimes. Motivated by the group-theoretic foundations of geometry established by the Göttingen school and by the central role of invariants in topology, we introduce a setting in which geometric organization emerges from the interplay between an invariant, idempotent operator µ and an angular […]