The homotopy operator of the Poincaré lemma and the exterior derivative satisfy a fermionic oscillator algebra with eigenvalues ±1, and split on complex manifolds into a pair of operators generating a dual Dolbeault bicomplex.
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The Poincare lemma, antiexact forms, and fermionic quantum harmonic oscillator
The homotopy operator of the Poincaré lemma and the exterior derivative satisfy a fermionic oscillator algebra with eigenvalues ±1, and split on complex manifolds into a pair of operators generating a dual Dolbeault bicomplex.