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

V.; F.

doi:https://doi.org/10.54216/JCFA.020204

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Volume 2 • Issue 2 • PP: 22-24 • 2023

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

V. Christianto ^1*

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,

F. Smarandache ²

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

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

* Corresponding Author.

DOI https://doi.org/10.54216/JCFA.020204

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Received: June 08, 2023 Accepted: December 15, 2023

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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 Poincar&eacute conjecture

References

[1] Christianto, V., Chandra, T. D., Smarandache, F. (Year). Godel, Escherian Staircase and Possibility of Quantum Wormhole With Liquid Crystalline Phase of Iced-Water - Part I: Theoretical Underpinning. BPAS Chemistry Section (Dec. 2023, in preparation)

[2] Perelman, G. (2003). The entropy formula for the Ricci flow and its geometric applications. …

[3] Perelman, G. (2003). Ricci flow with surgery on three-manifolds. …

[4] Perelman, G. (2003). Finite extinction time for the solutions to the Ricci flow on certain three-manifolds. …

[5] Emily E. Pocock, et al. Experimental and Computational Study of a Liquid Crystalline Dimesogen Exhibiting Nematic, Twist-Bend Nematic, Intercalated Smectic, and Soft Crystalline Mesophases. Molecules. 2021 Feb; 26(3): 532. DOI: 10.3390/molecules26030532

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Christianto, V., Smarandache, F.. "Exploring Non-Orientable Topology: Deriving the Poincaré Conjecture and possibility of experimental vindication with liquid crystal." Journal of Cosmology, Filaments and Astrobiology, vol. Volume 2, no. Issue 2, 2023, pp. 22-24. DOI: https://doi.org/10.54216/JCFA.020204

Christianto, V., Smarandache, F. (2023). Exploring Non-Orientable Topology: Deriving the Poincaré Conjecture and possibility of experimental vindication with liquid crystal. Journal of Cosmology, Filaments and Astrobiology, Volume 2(Issue 2), 22-24. DOI: https://doi.org/10.54216/JCFA.020204

Christianto, V., Smarandache, F.. "Exploring Non-Orientable Topology: Deriving the Poincaré Conjecture and possibility of experimental vindication with liquid crystal." Journal of Cosmology, Filaments and Astrobiology Volume 2, no. Issue 2 (2023): 22-24. DOI: https://doi.org/10.54216/JCFA.020204

Christianto, V., Smarandache, F. (2023) 'Exploring Non-Orientable Topology: Deriving the Poincaré Conjecture and possibility of experimental vindication with liquid crystal', Journal of Cosmology, Filaments and Astrobiology, Volume 2(Issue 2), pp. 22-24. DOI: https://doi.org/10.54216/JCFA.020204

Christianto V, Smarandache F. Exploring Non-Orientable Topology: Deriving the Poincaré Conjecture and possibility of experimental vindication with liquid crystal. Journal of Cosmology, Filaments and Astrobiology. 2023;Volume 2(Issue 2):22-24. DOI: https://doi.org/10.54216/JCFA.020204

V. Christianto, F. Smarandache, "Exploring Non-Orientable Topology: Deriving the Poincaré Conjecture and possibility of experimental vindication with liquid crystal," Journal of Cosmology, Filaments and Astrobiology, vol. Volume 2, no. Issue 2, pp. 22-24, 2023. DOI: https://doi.org/10.54216/JCFA.020204

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