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I'm reading Bott-Tu and they write the volume form on the unit n-sphere in $\Bbb{R}^n$ as $\sum_{i=1}^{n+1} (-1)^{i-1} x_i dx_1 ... \hat{dx_i} ... dx_{n+1}$, where juxtaposition of differential forms denotes the wedge product. What does $\hat{dx_i}$ mean?

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    $\begingroup$ It means that that factor is omited. $\endgroup$ – Rene Schipperus Oct 9 '17 at 3:22
  • $\begingroup$ in this context, it means that is the specific one-form that is NOT part of the product. $\endgroup$ – Will Jagy Oct 9 '17 at 3:22
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    $\begingroup$ also, the $n$-sphere is in $\mathbb R^{n+1}$ $\endgroup$ – Will Jagy Oct 9 '17 at 3:29
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I guess it is mentioned somewhere in the book: that means the specific one form $dx_i$ is omitted. For example,

$$ dx_1\cdots \hat{dx_5} \cdots dx_{10}= dx_1dx_2dx_3dx_4dx_6dx_7dx_8dx_9dx_{10}$$

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