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
$$A \wedge A \wedge A \wedge A \wedge A = \epsilon^{abcde}A_a A_b A_c A_d A_e$$?

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

 

[haushofer]

You should write
$$A \equiv A_i dx^i$$

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

$$A_{[a}A_b A_c A_d A_{e]}$$