What mathematics did Perelman use to prove Poicare's conjecture? Do you know any guide or any book?
You can start here.
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
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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