Question

what is the Poincaré Conjecture???explain

Answer 1

Answer:

Poincaré conjecture, in topology, conjecture—now proven to be a true theorem—that every simply connected, closed, three-dimensional manifold is topologically equivalent to S3, which is a generalization of the ordinary sphere to a higher dimension (in particular, the set of points in four-dimensional space that are ...

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Answer 2

Poincaré conjecture. A compact 2-dimensional surface without boundary is topologically homeomorphic to a 2-sphere if every loop can be continuously tightened to a point. The Poincaré conjecture asserts that the same is true for 3-dimensional spaces.

Equivalent to: Spherical space form conjecture; ...

Implied by: Geometrization conjecture; Zeeman ...