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Wedge product in tensor notation

  1. Apr 30, 2012 #1
    Is the following the definition of wedge product in tensor notation?

    Let [tex] A \equiv A_i [/tex] be a matrix one form. Then
    [tex]

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

    [/tex]?

    in 5 dimensions. This question is in reference to the winding number of maps.
     
  2. jcsd
  3. May 1, 2012 #2

    haushofer

    User Avatar
    Science Advisor

    You should write
    [tex]
    A \equiv A_i dx^i
    [/tex]

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

    [tex]
    A_{[a}A_b A_c A_d A_{e]}
    [/tex]
     
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