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Aug 2, 2021 at 11:54 vote accept G. Blaickner
Aug 2, 2021 at 11:34 answer added Tobias Diez timeline score: 7
Jul 31, 2021 at 16:15 comment added mme I don't think the bilinear map is an important part of the setup. What you want is a wedge product $\Omega^*(M,E) \otimes \Omega^*(M,F) \to \Omega^*(M, E \otimes F)$. Then you can simply apply $\mu$, because a linear bundle map E -> E' induces a map from E-valued forms to E'-valued forms. Phrased like this I believe there's a discussion of bundle-valued wedge products in Sharpe's differential geometry textbook, but I don't have access to a copy to check right now.
Jul 31, 2021 at 7:14 history edited G. Blaickner CC BY-SA 4.0
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Jul 31, 2021 at 6:57 history edited YCor CC BY-SA 4.0
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Jul 31, 2021 at 6:49 history edited G. Blaickner CC BY-SA 4.0
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Jul 31, 2021 at 6:43 history asked G. Blaickner CC BY-SA 4.0