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 Mat. Sb., 2001, Volume 192, Number 2, Pages 27–56 (Mi msb541)

Triangular de Rham cohomology of compact Kahler manifolds

A. Yu. Brudnyia, A. L. Onishchikb

a Ben-Gurion University of the Negev
b Yaroslavl State Technical University

Abstract: The de Rham $H^1_{DR}(M,G)$ 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 $M\times G$ 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 $H^1_{DR}(M,G)$ in terms of the cohomology of $M$ with values in the (Abelian) sheaves of flat sections of certain flat Lie algebra bundles with fibre $\mathfrak g$ (the tangent Lie algebra of $G$) or, equivalently, in terms of the harmonic forms on $M$ representing this cohomology is obtained.

DOI: https://doi.org/10.4213/sm541

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English version:
Sbornik: Mathematics, 2001, 192:2, 187–214

Bibliographic databases:

UDC: 515.176
MSC: Primary 14F40, 32Q15, 32L10; Secondary 14F05

Citation: A. Yu. Brudnyi, A. L. Onishchik, “Triangular de Rham cohomology of compact Kahler manifolds”, Mat. Sb., 192:2 (2001), 27–56; Sb. Math., 192:2 (2001), 187–214

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb541
• https://doi.org/10.4213/sm541
• http://mi.mathnet.ru/eng/msb/v192/i2/p27

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This publication is cited in the following articles:
1. Brudnyi A., “Solvable matrix representations of Kahler groups”, Differential Geom. Appl., 19:2 (2003), 167–191
2. D. N. Akhiezer, È. B. Vinberg, V. V. Gorbatsevich, V. G. Durnev, R. Zulanke, L. S. Kazarin, D. A. Leites, V. V. Serganova, V. M. Tikhomirov, “Arkadii L'vovich Onishchik (on his 70th birthday)”, Russian Math. Surveys, 58:6 (2003), 1245–1253
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