Poincaré conjecture
Table:
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.

Field	Geometric topology
Conjectured by	Henri Poincaré
Conjectured in	1904
First proof by	Grigori Perelman
First proof in	2006
Implied by

Geometrization conjecture
Zeeman conjecture[1]

Equivalent to

Spherical space form conjecture

Thurston elliptization conjecture

Generalizations	Generalized Poincaré conjecture

With reference to the table, judge whether the statement is entailed, neutral, or refuted according to the table. Conclude with JSON {"answer": "YOUR ANSWER"} — nothing else.

Assertion: Poincaré conjecture took over a century to be proven.

answer: entailed