Primitive stable representations in higher rank semisimple Lie groups

2015/04/30 by Инканг Ким, Sungwoon Kim, Kim, Inkang +1
Mathematics · #20E05 #22F30 #32G15 #Advanced Algebra and Geometry #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1504.08056

openalex publication_date 2015/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study primitive stable representations of free groups into higher rank semisimple Lie groups and their properties. Let Σ be a compact, connected, orientable surface (possibly with boundary) of negative Euler characteristic. We first verify the σ_mod-regularity for convex projective structures and positive representations. Then we show that the holonomies of convex projective structures and positive representations on Σ are all primitive stable if Σ has one boundary component.

Citations

• Representations and geometric structures
• McShane identities for Higher Teichmüller theory and the Goncharov-Shen potential

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