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Is $TS^n$ diffeomorphdiffeomorphic to an open subset of $\mathbb{R}^{2n}$

For what values of $n \neq 1,3,7$, is the tangent bundle $TS^n$ of the $n$_spher, is-sphere diffeomorphic to an open subset of $\mathbb{R}^{2n}$?

For what values of $n \neq 1,3,7$, the tangent bundle $TS^n$ of $n$_spher, is diffeomorphic to an open subset of $\mathbb{R}^{2n}$?

For what values of $n \neq 1,3,7$ is the tangent bundle $TS^n$ of the $n$-sphere diffeomorphic to an open subset of $\mathbb{R}^{2n}$?

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Ali Taghavi
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