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Filtrations on the log de Rham complex
Filtrations on the log de Rham complexopenaire +1 more source
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Decomposition of the de Rham complex
Proceedings of the Indian Academy of Sciences - Section A, 1990The proof by \textit{P. Deligne} and \textit{L. Illusie} [Invent. Math. 89, 247-270 (1987; Zbl 0632.14017)] of the degeneration of the \(E_ 1\)-term of the Hodge spectral sequence of a smooth variety X, after its reduction to the characteristic \(p\) case, is embellished by using explicit quasi- isomorphisms instead of working locally in the derived ...
Veeturi Srinivas
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Theoretical and Mathematical Physics(Russian Federation), 2013
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V V Zharinov
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
V V Zharinov
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De Rham theory of a simplicial complex
Functional Analysis and Its Applications, 1992D. Sullivan's basic result in rational homotopy theory is that integration of differential forms whose coefficients are \(Q\)-polynomials in the barycentric coordinates of a simplicial complex \(X\) induces an isomorphism between the cohomology of the de Rham-Sullivan commutative differential graded algebra \(A^*(X)\) and the singular cohomology \(H ...
I V Savel'Ev
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Stochastic Algebraic de Rham Complexes
Acta Applicandae Mathematica, 2003In this very interesting paper the author continues his study of extension of the de Rham complexes for finite dimensional compact manifolds \(M\) to the infinite dimensional manifolds -- the loop spaces associated to such manifolds. The work is an interplay between the topological properties of such manifolds and the stochastic properties associated ...
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1992
In this lecture we want to start with the definition and simple properties of the sheaf of (algebraic) logarithmic differential forms and of sheaves with logarithmic integrable connections, developed in [10]. The main examples of those will arise from cyclic covers (see Lecture 3). Even if we stay in the algebraic language, the reader is invited (see 2.
Hélène Esnault, Eckart Viehweg
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In this lecture we want to start with the definition and simple properties of the sheaf of (algebraic) logarithmic differential forms and of sheaves with logarithmic integrable connections, developed in [10]. The main examples of those will arise from cyclic covers (see Lecture 3). Even if we stay in the algebraic language, the reader is invited (see 2.
Hélène Esnault, Eckart Viehweg
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1982
Let U and V be open sets on a manifold. In Section 2, we saw that the sequence of inclusions $$U \cup V \leftarrow U\coprod V \Leftarrow U \cap V$$ gives rise to an exact sequence of differential complexes $$0 \to \Omega *(U \cup V) \to \Omega *(U) \oplus \Omega *(V) \to \Omega *(U \cap V) \to 0$$ called the Mayer—Vietoris sequence.
Raoul Bott, Loring W. Tu
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Let U and V be open sets on a manifold. In Section 2, we saw that the sequence of inclusions $$U \cup V \leftarrow U\coprod V \Leftarrow U \cap V$$ gives rise to an exact sequence of differential complexes $$0 \to \Omega *(U \cup V) \to \Omega *(U) \oplus \Omega *(V) \to \Omega *(U \cap V) \to 0$$ called the Mayer—Vietoris sequence.
Raoul Bott, Loring W. Tu
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THE DE RHAM COMPLEX ON INFINITE DIMENSIONAL MANIFOLDS
The Quarterly Journal of Mathematics, 1987The de Rham complex of a smooth manifold is called split if the space of n-forms \(\Omega^ n\) can be decomposed as \(\Omega^ n=B^ n\oplus H^ n\oplus \tilde B^{n+1}\) where \(B^ n=d(\Omega^{n+1})\) is the space of coboundaries in \(\Omega^ n\), \(H^ n\subset \ker (d)\) is the cohomology in dimension n and \(\tilde B^{n+1}\) is a subspace mapped ...
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Variations on the de Rham complex
1999Summary: Familiar identities with grad, div, and curl may be framed as the de Rham complex on an open set in Euclidean space. The corresponding complex on the three-sphere, when considered in a vector form, leads naturally to the Bernstein-Gelfand-Gelfand complex in representation theory.
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