Rigid representations of Kählerian fundamental groups
type: Item
instance of: scholarly article
title: Rigid representations of Kählerian fundamental groups
zbMATH Open document ID: 0731.53061
author: Kevin Corlette
published in: Journal of Differential Geometry
publication date: 1991-01-01T00:00:00Z
review text: It is known that cocompact lattices in a semisimple Lie group have no deformations, provided the group has no local three-dimensional factors. This paper is devoted to the study of the local rigidity in the context of locally symmetric manifolds. More precisely, the main purpose is to prove the following Theorem: Suppose that P is a flat principal \(G_{{\mathbb{R}}}\)-bundle over a compact Kähler manifold M with vol(P)\(\neq 0\), and assume that \(G_{{\mathbb{R}}}/K\) is not of the form U(n,1)/U(n)\(\times U(1)\) or \(SO(2n+1,2)/S(O(2n+1)\times O(2)).\) Then the monodromy homomorphism of the fundamental group of M into \(G_{{\mathbb{R}}}\) is locally rigid as a homomorphism into the complexification of \(G_{{\mathbb{R}}}\). Here \(G_{{\mathbb{R}}}\) is a simple real algebraic group acting by isometries on the irreducible bounded symmetric domain \(G_{{\mathbb{R}}}/K\).
reviewed by: Neda Bokan
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 4209027
zbMATH Keywords: bounded symmetric domain
zbMATH Keywords: characteristic classes
zbMATH Keywords: differential graded Lie algebra
zbMATH Keywords: local rigidity
zbMATH Keywords: locally symmetric manifolds
zbMATH Keywords: compact Kähler manifold
zbMATH Keywords: monodromy homomorphism
Wikidata QID: Q115181691
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214446037
OpenAlex ID: W1519243077
DOI: 10.4310/JDG/1214446037
description: scientific article; zbMATH DE number 4209027