What mathematics did Perelman use to prove Poicare's conjecture? Do

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Grigori Perelman utilized Ricci flow to prove the Poincaré conjecture, building upon the foundational work of Richard Hamilton. For those seeking further understanding, the Wikipedia page on the Poincaré conjecture serves as a comprehensive starting point. A recommended resource for deeper study is the book "Ricci Flow and the Poincaré Conjecture" available on Amazon. This discussion emphasizes the importance of accessible resources for complex mathematical topics.

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  • Differential geometry
  • Topology
  • Ricci flow
  • Mathematical proofs
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  • Study the principles of Ricci flow in detail
  • Explore Richard Hamilton's contributions to differential geometry
  • Read "Ricci Flow and the Poincaré Conjecture" for in-depth analysis
  • Investigate advanced topics in topology related to the Poincaré conjecture
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Mathematicians, graduate students in mathematics, and anyone interested in advanced geometric topology and the Poincaré conjecture.

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What mathematics did Perelman use to prove Poicare's conjecture? Do you know any guide or any book?
 
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Unless you are a specialist in differential geometry and topology, nobody's answer will be any more specific than the Wikipedia explanation. Perelman primarily used Ricci flow, as did Richard Hamilton before him. If you want a book, see
https://www.amazon.com/dp/0821843281/?tag=pfamazon01-20

N.B. Please don't be so quick to bash the other posters for recommending Wikipedia. They're trying to help, and it is the most helpful source for this topic for all but a tiny fraction of mathematicians. It doesn't mean that they're "not smart enough" to answer.
 

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