Degenerations of k-positive surface group representations

2021/06/10 by Jonas Beyrer, Beyrer, Jonas, Beatrice Pozzetti +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #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.2106.05983

openalex publication_date 2021/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce k-positive representations, a large class of \1,…,k\--Anosov surface group representations into PGL(E) that share many features with Hitchin representations, and we study their degenerations: unless they are Hitchin, they can be deformed to non-discrete representations, but any limit is at least (k-3)-positive and irreducible limits are (k-1)-positive. A major ingredient, of independent interest, is a general limit theorem for positively ratioed representations.

Cited by

• Positive surface group representations in PO(p,q)

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