Geometric Poincaré Lemma

Abstract

A geometric version of the Poincaré 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.

arXiv comment13 pages, 1 figure

Cited by in corpus (1)

• The Poincare lemma, antiexact forms, and fermionic quantum harmonic oscillator