Journal of Cosmology, Filaments and Astrobiology JCFA 2834-0221 10.54216/JCFA https://www.americaspg.com/journals/show/2338 2022 2022 Malang Institute of Agriculture (IPM), Jl. Soekarno-Hatta, Malang, Indonesia V. Christianto Department of Mathematics and Sciences, University of New Mexico–Gallup, Gallup, NM, USA F. Smarandache 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. 2023 2023 22 24 10.54216/JCFA.020204 https://www.americaspg.com/articleinfo/32/show/2338