The Poincar'e conjecture – a problem formulated 120 years ago by the French mathematician Henri Poincar'e, and solved at the beginning of this century by G. Perelman – has been one of the major issues of modern mathematics. It simply states that any three-dimensional space which is closed and without holes can be deformed into a three-dimensional sphere. The purpose of this article is to briefly review what we know today about the Poincar'e conjecture and its related problems in dimension 3.
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