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LSpice
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Why are $S^3-K$ and $\operatorname{SL}(2,\mathbb R)/{\operatorname{SL}(2, \mathbb Z)}$ diffeomorphic? Here $K$ is a trefoil knot in $S^3$

rewrote the title with latex. changed "trefoil" to "trefoil knot"
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Why S^3are $S^3-KK$ and SL$\operatorname{SL}(2,R\mathbb R)/\operatorname{SL}(2,Z \mathbb Z) are$ diffeomorphic? Here K$K$ is a trefoil knot in S^3.$S^3$

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Yuchen Liu
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Why S^3-K and SL(2,R)/SL(2,Z) are diffeomorphic? Here K is a trefoil in S^3.

I've heard this result from my differential manifold class, and I don't know how to prove it.

Does anyone know how to construct such diffeomorphism? Please tell me, thanks a lot.

Any comments are welcome.