Geometric Poincaré Lemma

Published 1 Jan 2011 in math.AT and math.DG | (1101.0313v2)

Abstract: 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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Jenny Harrison

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