منابع مشابه
Algebraic de Rham cohomology
Before we continue, we need to point out some properties of algebraic de Rham cohomology. In other words, we will first prove some of the axioms before introducing the trace map and cohomology classes. Note that the axioms of a Weil cohomology theory do not provide for the existence of cohomology groups defined for nonprojective varieties, but that we may use the fact that they are defined for ...
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The goal of this short paper is to give a slightly different perspective on the comparison between crystalline cohomology and de Rham cohomology. Most notably, we reprove Berthelot’s comparison result without using pd-stratifications, linearisations, and pd-differential operators. Crystalline cohomology is a p-adic cohomology theory for varieties in characteristic p created by Berthelot [Ber74]...
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(Here we really mean the integral over Σ of the form obtained by pulling back ω under the inclusion map). Now suppose we have two such submanifolds, Σ0 and Σ1, which are (smoothly) homotopic. That is, we have a smooth map F : Σ × [0, 1] → M with F |Σ×{i} an immersion describing Σi for i = 0, 1. Then d(F∗ω) is a (k + 1)-form on the (k + 1)-dimensional oriented manifold with boundary Σ × [0, 1], ...
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We briefly review differential forms on manifolds. We prove homotopy invariance of cohomology, the Poincaré lemma and exactness of the Mayer–Vietoris sequence. We then compute the cohomology of some simple examples. Finally, we prove Poincaré duality for orientable manifolds.
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We define quantum exterior product ∧h and quantum exterior differential dh on Poisson manifolds, of which symplectic manifolds are an important class of examples. Quantum de Rham cohomology is defined as the cohomology of dh. We also define quantum Dolbeault cohomology. Quantum hard Lefschetz theorem is proved. We also define a version of quantum integral, and prove the quantum Stokes theorem. ...
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ژورنال
عنوان ژورنال: Communications in Analysis and Geometry
سال: 2010
ISSN: 1019-8385,1944-9992
DOI: 10.4310/cag.2010.v18.n2.a4