Last Updated：2025/11/24

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(of a knot k) That no nontrivial Dehn surgery along k in the 3-sphere yields a simply connected manifold.

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Property P

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Source Word

Property P

Proper noun

of a knot k

(of a knot k) That no nontrivial Dehn surgery along k in the 3-sphere yields a simply connected manifold.

Japanese Meaning

結び目 k に対して、3次元球面上で非自明な Dehn 手術を施しても、得られる多様体が単連結（全ての閉曲線が収縮可能）にならない性質。

What is this buttons?

Many knot theorists investigate whether a given knot has Property P, since that condition prevents any nontrivial Dehn surgery in the 3-sphere from yielding a simply connected manifold.

Google Translation / DeepL Translation

多くの結び目理論家は、与えられた結び目が「3-球内のその結び目に沿った自明でないドイン手術が単連結多様体を生じさせない」という性質を持つかどうかを調べている。

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Sense（1）

(of a knot k) That no nontrivial Dehn surgery along k in the 3-sphere yields a simply connected manifold.

Details

Property P

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Property P

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