# Poincaré conjecture

theorem in geometric topology that every simply connected, closed 3-manifold is homeomorphic to the 3-sphere

In mathematics, the **Poincaré conjecture** is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space. The conjecture states: *Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.*

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## Quotes

edit- Posed in 1904 by Henri Poincaré, the leading mathematician of his era and among the most gifted of all time, the Poincaré conjecture is a bold guess about nothing less than the potential shape of our own universe.
- Donal O'Shea (30 October 2008).
*The Poincaré Conjecture: In Search of the Shape of the Universe*. Penguin Books Limited. pp. 13. ISBN 978-0-14-190034-6.

- Donal O'Shea (30 October 2008).