Last Updated：2025/11/23

The theorem that the only simply connected, closed 3-dimensional manifold is a sphere.

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Poincaré conjecture

Source Word

Poincaré conjecture

Proper noun

The theorem that the only simply connected, closed 3-dimensional manifold is a sphere.

Japanese Meaning

唯一の単純連結で閉じた３次元多様体は球面であるという定理。

After a century of attempts, the successful proof of the Poincaré conjecture transformed our understanding of three-dimensional spaces.

1世紀にわたる試みの末、唯一の単連結で閉じた三次元多様体が球体であるという定理の証明の成功は、三次元空間の理解を一変させた。

Sense（1）

The theorem that the only simply connected, closed 3-dimensional manifold is a sphere.

the Poincaré conjecture

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