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Review Papers | Mathematics | India | Volume 12 Issue 7, July 2023 | Popularity: 6.7 / 10

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An Elementary Proof of the Poincare

Shivam Kumar

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

DOI: https://www.doi.org/10.21275/SR23719203459

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