Representations of Fundamental Groups of Compact Kahler Manifolds in Solvable Matrix Groups

Alexander Brudnyi

Home/Archive/arXiv

arXiv · math/9911080

Representations of Fundamental Groups of Compact Kahler Manifolds in Solvable Matrix Groups

Alexander Brudnyi

View original source ↗Read source document ↗Export metadata ↓

Abstract

In the paper we prove a factorization theorem for representations of fundamental groups of compact Kähler manifolds ({\em Kähler groups}) into solvable matrix groups. We apply this result to prove that the universal covering of a compact Kähler manifold with a residually solvable fundamental group is holomorphically convex.

Explore related subjects

math.CV

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Alexander Brudnyi. 2001-04-27. Representations of Fundamental Groups of Compact Kahler Manifolds in Solvable Matrix Groups. https://arxiv.org/abs/math/9911080

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

On the Ohsawa-Takegoshi $L^2$ extension theorem and removable singularities of plurisubharmonic functions

The celebrated Ohsawa--Takegoshi extension theorem for $L^2$ holomorphic functions on bounded pseudoconvex domains in $\mathbb C^n$ is a fundamental result in the fields of complex analysis and algebraic geometry. In 1995, Ohsawa conjectured that the theorem holds more generally on bounded complete Kähler domains in $\mathbb C^n$. Recently, Chen, Wu and Wang confirmed this conjecture in a special case. In this paper, we extend their result to the case of holomorphic sections of twisted canonical bundles over relatively compact complete Kähler domains in Stein manifolds. As an application, we establish a Hartogs-type extension theorem for plurisubharmonic functions across compact complete pluripolar sets. This result complements a classical theorem of Shiffman and may be regarded as a plurisubharmonic analogue of the Skoda--El Mir extension theorem, thereby filling a gap that appears to have remained open in the literature since at least 1985.

math.CV↗

arXiv2026

The real analytic structure of the Teichmüller space of circle diffeomorphisms with Zygmund continuous derivatives

We apply the methods of simultaneous uniformization and composition operators on Besov spaces to the Teichmüller space $T^Z$ of circle diffeomorphisms with Zygmund continuous derivatives. As consequences, we obtain the following: (1) a new proof of the correspondence between quasiconformal self-homeomorphisms of the unit disk with complex dilatations of linear decay order and their quasisymmetric extensions to the unit circle with regularity in the Zygmund continuously differentiable class; (2) a real-analytic equivalence of $T^Z$ with the real Banach space of Zygmund continuous functions on the unit circle.

math.CV↗

arXiv2026

The Oka principle for holomorphic fibre bundles of Holder-Zygmund classes on strongly pseudoconvex domains

Let $\overline Ω$ be a compact strongly pseudoconvex domain with smooth boundary in a Stein manifold, and let $h:Z\to \overline Ω$ be a fibre bundle of Hölder-Zygmund class $Λ^r$, $r>0$, which is holomorphic over $Ω$. Assuming that the fibre is an Oka manifold, we prove that every continuous section $f_0:\overline Ω\to Z$ is homotopic to a section $f_1:\overline Ω\to Z$ of class $Λ^r(\overline Ω)$ which is holomorphic on $Ω$. We also establish the parametric h-principle in this context. As an application, we obtain the Oka principle for the classification of vector bundles and principal bundles of Hölder-Zygmund classes on such domains.

math.CV↗