Exploring Non-Orientable Topology: Deriving the Poincaré Conjecture and possibility of experimental vindication with liquid crystal

V. Christianto¹ , F. Smarandache²

¹Malang Institute of Agriculture (IPM), Jl. Soekarno-Hatta, Malang, Indonesia

² Department of Mathematics and Sciences, University of New Mexico–Gallup, Gallup, NM, USA

Emails: victorchristianto@gmail.com; smarand@unm.edu

Abstract

This review investigates the potential of non-orientable topology as a fundamental framework for understanding the Poincaré conjecture and its implications across various scientific disciplines. Integrating insights from Dokuchaev (2020), Rapoport, Christianto, Chandra, Smarandache (under review), and other pioneering works, this article explores the theoretical foundations linking non-orientable spaces to resolving the Poincaré conjecture and its broader implications in theoretical physics, geology, cosmology, and biology.

Keywords: non-orientable topology; liquid crystal; Poincaré conjecture