= Metric independence of curvature Dolbeault powers
{title2=$\alpha(E)^k=[\Theta^k]$}
Composition of <endomorphisms> and <wedge product of differential forms> give the class $[\Theta^k]\in H^k(M,\Omega_M^k\otimes\operatorname{End}E)$. Even total degree of <vector-bundle curvature> and the noncommutative telescoping identity give $\Theta_1^k-\Theta_0^k=\bar\partial\sum_{j=0}^{k-1}\Theta_1^j a\Theta_0^{k-1-j}$ whenever $\Theta_1-\Theta_0=\bar\partial a$. Thus all powers are metric independent; no commutativity of <endomorphisms> is assumed.
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