An Outreach Note on the Poincare Conjecture for Non-specialists
DOI:
https://doi.org/10.29020/nybg.ejpam.v17i3.5351Keywords:
3-manifolds, homotopy spheres, differential structuresAbstract
The Poincare Conjecture, a problem formulated by the French mathematician Henri Poincare more than a century ago, has been one of the main challenge of modern mathematics. It states that any three-dimensional space which is closed on itself and without holes can be deformed into a sphere of dimension 3. Even if the conjecture was solved at the beginning of this century, it still remains a mysterious, appealing and intriguing problem worth to be further studied in detail. The purpose of this short popularizing note is, on the one hand, to provide a quick overview for non-experts of what we know today about the Poincare Conjecture and its related problems in dimension 3, and, on the other hand, to explain why it has represented a central problem in mathematics.
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