Geometric Poincar\'e Lemma
Algebraic Topology
2015-03-17 v2 Differential Geometry
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.
Cite
@article{arxiv.1101.0313,
title = {Geometric Poincar\'e Lemma},
author = {Jenny Harrison},
journal= {arXiv preprint arXiv:1101.0313},
year = {2015}
}
Comments
13 pages, 1 figure