RUS  ENG
Full version
JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb., 2001 Volume 192, Number 2, Pages 27–56 (Mi sm541)

This article is cited in 1 paper

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.

UDC: 515.176

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

Received: 16.02.2000

DOI: 10.4213/sm541


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

Bibliographic databases:


© Steklov Math. Inst. of RAS, 2025