Invariant functions on Lie groups and Hamiltonian flows of surface group representations
type: Item
instance of: scholarly article
title: Invariant functions on Lie groups and Hamiltonian flows of surface group representations
zbMATH Open document ID: 0619.58021
DOI: 10.1007/BF01389091
author: William M. Goldman
published in: Inventiones Mathematicae
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143369
review text: In a previous paper [Adv. Math. 54, 200--225 (1984; Zbl 0574.32032)], the author has shown that if \(\pi\) is the fundamental group of a closed oriented surface \(S\) and \(G\) is a Lie group satisfying very general conditions, then the space \(\Hom(\pi,G)/G\) of conjugacy classes of representations \(\pi\to G\) has a natural symplectic structure. (This structure generalizes the Weil-Petersson Kähler form on Teichmüller spaces, the Kähler form on Jacobi varieties of Riemann surfaces homeomorphic to \(S\) and other well-known symplectic structures.) The purpose of this paper is to investigate the geometry of this symplectic structure with the aid of a natural family of functions on \(\Hom(\pi,G)/G\).
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 57M05
Mathematics Subject Classification ID: 43A99
Mathematics Subject Classification ID: 22E99
Mathematics Subject Classification ID: 58J70
zbMATH DE Number: 4005191
zbMATH Keywords: invariant functions on Lie groups
zbMATH Keywords: Hamiltonian flows
zbMATH Keywords: surface group representations
zbMATH Keywords: Weil-Petersson Kähler form on Teichmüller spaces
zbMATH Keywords: Kähler form on Jacobi varieties
reviewed by: Paul Godin
MaRDI profile type: Publication
Wikidata QID: Q115393632
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description: scientific article; zbMATH DE number 4005191