Triangular de Rham cohomology of compact Kahler manifolds
- Ben-Gurion University of the Negev (Israel)
- Yaroslavl State Technical University, Yaroslavl (Russian Federation)
The de Rham H{sup 1}{sub DR}(M,G) of a smooth manifold M with values in a group Lie G is studied. By definition, this is the quotient of the set of flat connections in the trivial principal bundle MxG by the so-called gauge equivalence. The case under consideration is the one when M is a compact Kahler manifold and G is a soluble complex linear algebraic group in a special class containing the Borel subgroups of all complex classical groups and, in particular, the group of all triangular matrices. In this case a description of the set H{sup 1}{sub DR}(M,G) in terms of the cohomology of M with values in the (Abelian) sheaves of flat sections of certain flat Lie algebra bundles with fibre g (the tangent Lie algebra of G) or, equivalently, in terms of the harmonic forms on M representing this cohomology is obtained.
- OSTI ID:
- 21205589
- Journal Information:
- Sbornik. Mathematics, Vol. 192, Issue 2; Other Information: DOI: 10.1070/SM2001v192n02ABEH000541; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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