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https://math.stackexchange.com/questions/1806437/poincare-lemma-for-compact-vertical-supports-in-bott-tu
Poincare lemma for compact vertical supports in Bott & Tu. Ask Question Asked 3 years, 8 months ago. ... Thanks for contributing an answer to Mathematics Stack Exchange! ... The Poincare Lemma for Compactly Supported Cohomology. 49.
https://mufan-li.github.io/poincare_inequality/
Dec 30, 2017 · Quick aside: we say a function has compact support if the set has compact closure. This implies near the boundary.. Observe that the inequality simply bounds the -norm of a function in terms of the -norm of its gradient instead.Note the compact support here is an important assumption when we are integrating with respect to the Lebesgue measure.
http://tungsteno.io/post/lem-poincare_lemma/
Tungsteno is a project whose goal is to make mathematics accessible to everybody, completely free, based on open collaboration and the best pedagogical tools
https://mathoverflow.net/questions/180451/poincare-lemma-for-non-smooth-differentiable-forms
Poincare lemma for non-smooth differentiable forms. Ask Question ... The Poincare lemma is almost always formulated for differential forms with smooth coefficients (or sometimes for currents that have distributional coefficients). ... states that there is a continuous function $\psi:\mathbb R^2 \to\mathbb R$ with compact support such that the ...
http://www.math.columbia.edu/~rzhang/files/PoincareDuality.pdf
POINCARE DUALITY ROBIN ZHANG Abstract. This expository work aims to provide a self-contained ... Lemma 2.1. Let Mbe a manifold of dimension nwith a compact sucompact subset AˆM. De ne M R:= S x2M f x 2H ... homology with compact support, we quickly give a de nition below before proceeding onto the lemma statement. De nition 2.3.
https://en.wikipedia.org/wiki/Differential_forms_on_a_Riemann_surface
Comment on differential forms with compact support. Note that if ω has compact support, so vanishes outside some smaller rectangle (a 1,b 1) × (c 1,d 1) with a < a 1 < b 1 <b and c < c 1 < d 1 < d, then the same is true for the solution f(x,y). So the Poincaré lemma for 1-forms holds with this additional conditions of compact support.
https://en.wikipedia.org/wiki/Poincar%C3%A9_duality
In mathematics, the Poincaré duality theorem, named after Henri Poincaré, is a basic result on the structure of the homology and cohomology groups of manifolds.It states that if M is an n-dimensional oriented closed manifold (compact and without boundary), then the kth cohomology group of M is isomorphic to the (−)th homology group of M, for all integers k
https://arxiv.org/abs/1101.0313v1
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 ...
https://arxiv.org/abs/1101.0313
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.
https://en.wikipedia.org/wiki/Integration_along_fibers
Proposition — Let : → be an oriented vector bundle over a manifold and ∗ the integration along the fiber. Then ∗ is ∗ ()-linear; i.e., for any form β on B and any form α on E with vertical-compact support, ∗ (∧ ∗) = ∗ ∧. If B is oriented as a manifold, then for any form α on E with vertical compact support and any form β on B with compact support,
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