Question

The Poincaré Conjecture

Answer 1

Answer:

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

Explanation:

• First proof by: Grigori Perelman
• First proof in: 2006
• Field: Geometric topology
• Generalizations: Generalized Poincaréconjecture
• Equivalent to: Spherical space formconjecture; Thurston elliptization conjecture
• Implied by: Geometrization conjecture; Zeeman conjecture;

Answer 2

Answer:

In mathematics, poincare conjecture is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space.