Wedge product in tensor notation

[praharmitra]

Is the following the definition of wedge product in tensor notation?

Let A \equiv A_i be a matrix one form. Then
<br /> <br /> A \wedge A \wedge A \wedge A \wedge A = \epsilon^{abcde}A_a A_b A_c A_d A_e<br /> <br />?

in 5 dimensions. This question is in reference to the winding number of maps.

 

[haushofer]

You should write
<br /> A \equiv A_i dx^i<br />

i.e. the wedge product is defined on the basis. Then your wedge product has as components

<br /> A_{[a}A_b A_c A_d A_{e]}<br />