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Geometric Poincar\'e Lemma

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arxiv 1101.0313 v2 pith:XPUB54RM submitted 2011-01-01 math.AT math.DG

Jenny Harrison This is my paper · ORCID
classification math.ATmath.DG
keywords differentialcompactgeometriclemmapoincarsupporttheoremapplications
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A geometric version of the Poincar\'e Lemma is established for the topological vector space of differential chains. In particular, every differential k-cycle with compact support in a contractible open subset U of a smooth n-manifold M is the boundary of a differential (k+1) -chain with compact support in U. Applications include generalizations of the Intermediate Value Theorem and Rolle's Theorem.

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  1. The Poincare lemma, antiexact forms, and fermionic quantum harmonic oscillator

    math.DG 2019-08 accept novelty 5.0 of 10

    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 b...

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