Poincaré conjecture

What was discovered

Every closed, simply connected 3-manifold is homeomorphic to the three-dimensional sphere. It was the central problem of topology for a century, until its proof by Perelman.

The analogues in dimension 5 or higher were proved by Smale (1961) and in dimension 4 by Freedman (1982).

What it led to

• the topology of manifolds
• Thurston's geometrisation
• Hamilton's Ricci flow
• Perelman's proof (2003)

Built on

• Algebraic topology: homology and fundamental group1895
• Poincaré homology

Made possible

• Proof of the Poincaré and geometrization conjectures2002-2003

Links