On the Teichmüller stack of homogeneous spaces of SL(2,C)

2021/02/23 by Théo Jamin, Jamin, Théo
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Character (mathematics) #Combinatorics #Complex Variables (math.CV) #Computer science #FOS: Mathematics #Geometric and Algebraic Topology #Geometry #Holonomy #Homogeneous #Homotopy and Cohomology in Algebraic Topology #Mathematics #Pure mathematics #Representation (politics) #Representation Theory (math.RT) #Stack (abstract data type) #Variety (cybernetics) #math.AG #math.CV #math.RT

paper · pdf · doi:10.48550/arxiv.2102.12364

arxiv created 2021/02/23 · openalex publication_date 2021/02/23 · arxiv updated 2021/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that the (admissible) character stack, which is a stack version of the character variety, is an open substack of the Teichmüller stack of homogeneous spaces of SL(2,C). We show that the tautological family over the representation variety, given by deforming the holonomy, is always a complete family. This is a generalisation of the work of E. Ghys about deformations of complex structures these homogeneous spaces.

Citations

• Differential Geometry, Lie Groups, and Symmetric Spaces
• SL(n,C)- Representation spaces of Knot Groups
• Complex Analytic Coordinates in Almost Complex Manifolds

Related

• Bending Teichmüller spaces and character varieties
• Teichmüller spaces, polynomial loci, and degeneration in spaces of algebraic correspondences
• The Teichmüller Stack
• Higher Teichmüller Spaces: from SL(2,R) to other Lie groups
• Generalizations of the Eierlegende-Wollmilchsau