Search results for "Chern–Weil homomorphism"

showing 5 items of 5 documents

Equivariant cohomology, Fock space and loop groups

2006

Equivariant de Rham cohomology is extended to the infinite-dimensional setting of a loop subgroup acting on a loop group, using Hida supersymmetric Fock space for the Weil algebra and Malliavin test forms on the loop group. The Mathai–Quillen isomorphism (in the BRST formalism of Kalkman) is defined so that the equivalence of various models of the equivariant de Rham cohomology can be established.

Pure mathematicsChern–Weil homomorphismGroup cohomologyMathematical analysisGeneral Physics and AstronomyStatistical and Nonlinear PhysicsWeil algebraMathematics::Algebraic TopologyCohomologyMathematics::K-Theory and HomologyLoop groupDe Rham cohomologyEquivariant mapEquivariant cohomologyMathematics::Symplectic GeometryMathematical PhysicsMathematicsJournal of Physics A: Mathematical and General
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Algebraic de Rham Cohomology

2017

Let k be a field of characteristic zero. We are going to define relative algebraic de Rham cohomology for general varieties over k, not necessarily smooth.

Hodge conjecturePure mathematicsChern–Weil homomorphismMathematics::K-Theory and HomologyGroup cohomologyCyclic homologyDe Rham cohomologyEquivariant cohomologyMathematics::Algebraic TopologyCohomologyMathematicsMotivic cohomology
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Holomorphic de Rham Cohomology

2017

We are going to define a natural comparison isomorphism between algebraic de Rham cohomology and singular cohomology of varieties over the complex numbers with coefficients in \(\mathbb {C}\). The link is provided by holomorphic de Rham cohomology, which we study in this chapter.

Pure mathematicsMathematics::Algebraic GeometryChern–Weil homomorphismMathematics::K-Theory and HomologyCup productHodge theoryCyclic homologyDe Rham cohomologyEquivariant cohomologyMathematics::Algebraic TopologyČech cohomologyCohomologyMathematics
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On globally generated vector bundles on projective spaces II

2014

Extending a previous result of the authors, we classify globally generated vector bundles on projective spaces with first Chern class equal to three.

Pure mathematicsAlgebra and Number TheoryChern–Weil homomorphismChern classComplex projective spaceMathematical analysisVector bundleMathematics - Algebraic GeometryLine bundleFOS: MathematicsProjective spaceTodd classSettore MAT/03 - GeometriaAlgebraic Geometry (math.AG)Splitting principleMathematicsGlobally generated Vector bundles Projective Space
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Chern classes of the moduli stack of curves

2005

Here we calculate the Chern classes of ${\bar {\mathcal M}}_{g,n}$, the moduli stack of stable n-pointed curves. In particular, we prove that such classes lie in the tautological ring.

Pure mathematicsChern classChern–Weil homomorphismGeneral MathematicsMathematical analysisCharacteristic classModuliModuli of algebraic curvesMathematics - Algebraic GeometryMathematics::Algebraic GeometryGenus (mathematics)FOS: Mathematicschern classes moduli stackTodd classSettore MAT/03 - GeometriaAlgebraic Geometry (math.AG)MathematicsStack (mathematics)
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