International Journal of Science and Research (IJSR)

International Journal of Science and Research (IJSR)
Call for Papers | Fully Refereed | Open Access | Double Blind Peer Reviewed

ISSN: 2319-7064


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Review Papers | Mathematics | India | Volume 12 Issue 7, July 2023 | Rating: 5.1 / 10


An Elementary Proof of the Poincare

Shivam Kumar [3]


Abstract: We provide a comprehensive analysis and (simple) proof of Poincare's conjecture, a fundamental problem in topology. The conjecture asserts that any compact, smooth 3-manifold with the same homotopy type as the 3-sphere (S3) is necessarily diffeomorphic to S3 itself. Index Terms-Poincare's conjecture, compact manifolds, smooth manifolds, homotopy equivalence, diffeomorphism, 3-manifold, 3-sphere, topology, differential topology, algebraic topology.


Keywords: Poincare's Conjecture, topology, homotopy, sphere


Edition: Volume 12 Issue 7, July 2023,


Pages: 2230 - 2231


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