Notation reference: what does $\hat{dx}$ mean, where $dx$ is a differential form?

Question

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?

in this context, it means that is the specific one-form that is NOT part of the product. — Will Jagy, Oct 09 '17 at 03:22

score 1 · Answer 1 · answered Oct 09 '17 at 03:30

1

I guess it is mentioned somewhere in the book: that means the specific one form $dx_i$ is omitted. For example,

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

answered Oct 09 '17 at 03:30

Notation reference: what does $\hat{dx}$ mean, where $dx$ is a differential form?

1 Answers1