A new construction of characteristic classes of foliations (Q1174488)
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scientific article; zbMATH DE number 8849
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new construction of characteristic classes of foliations |
scientific article; zbMATH DE number 8849 |
Statements
A new construction of characteristic classes of foliations (English)
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25 June 1992
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A codimension-\(q\) foliation \(F\) of a manifold \(M\) with a trivialization \(X\) of the normal bundle is considered. A graded subalgebra \(C(F,X)\) of the exterior algebra \(A(M)\) of \(M\) is constructed. The injection of \(C(F,X)\) into \(A(M)\) determines on the \(c\) cohomology level a finitely dimensional subalgebra \(HC(F)\) of the de Rham cohomology algebra of \(M\). \(HC(F)\) contains all the characteristic classes of \(F\) as defined by Bernstein and Rosenfeld, Bott and Haefliger, and Fuks. The corresponding universal construction is performed.
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foliation
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characteristic classes
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de Rham cohomology
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universal algebra
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