Questions tagged [differential-forms]
A differential form $ \omega$ is a section of the exterior algebra $\Lambda^* T^* X$ of a cotangent bundle,
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Differential ideals of Pfaffian forms on jet bundles (Integrability)
(I asked this question on math.stackexchange, but got no reaction in several weeks. So, my conclusion is, that it is harder to answer than I thought, and maybe admissible for the attribute 'research ...
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differential forms in double field theory
In double field theory, there are 'double differential forms' meaning that the standard 1-forms $d x^i$ generate an algebra over functions depending on both of the double coordinates
$x^i$ and $\tilde ...
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Homology of a region of the plane
This is related to this MO question, I don't know if it's really "research-level". As in that question, let $U$ be a domain of the complex plane $\mathbb{C}$, i.e. an open connected subset. Let
$$ \...
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Non-continuous differentiability for differential forms
Generally when working with differential forms, one assumes that they are continuously differentiable, i.e. $C^r$ for some $1\le r \le \infty$. Under this hypothesis, one can define the exterior ...
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Analytic version of the Cartan lemma
Assume that $\beta$ is a real analytic 2-form on an analytic manifold $M$ and $\alpha$ is an analytic non vanishing 1-form on $M$. Assume that $\beta \wedge \alpha=0$. Is there an analytic 1-form $\...
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Restriction of a line bundle to a two-cycle
I am reading a paper on Chiral Differential Operators
http://arxiv.org/pdf/hep-th/0604179v3.pdf
and it says on page 23 that a line bundle over a manifold C can be characterized completely by its ...
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Residues and Mittag-Leffler sequence
Let $X$ be a compact Riemann surface, $\omega$ a meromorphic differential on $X$ and $f$ a meromorphic function on $X$ with poles only over the points $P_1,\dots,P_d$. The product $\;f\cdot\omega\;$ ...
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existence of meromorphic differentials with non vanishing residues
Let $X$ be a smooth projective variety over a field $k$ of characteristic zero and let $D$ be a simple normal crossing divisor on $X$, with irreducible components $D_i$.
Does there exist a nonzero ...
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(n-1)-dimensional normal currents and Smirnov's paper
I don't know much about currents, but I saw a paper of Smirnov which seems relevant to a problem I am working on. In the very last paragraph of page 848 of the following paper
http://www.unige.ch/~...
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$\infty$-forms and $\infty$-plectic geometry
Can you have $\infty$-forms on infinite-dimensional manifolds or elsewhere and what are they used for?
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When is the module of Kahler volume forms torsion-free?
Let $R$ be a commutative algebra over a field $k$. Denote the $R$-module of Kahler differentials by $\Omega^1_kR$; this is the $R$-module generated by symbols of the form $da$, $a\in R$, and ...
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superdiff forms and tensors
Where is it written that symmetric tensors (i.e. with multiindices)
occur as the coefficient functions of super differential forms
or rather odd differential forms?
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