SL(2;R)-representations of a Brieskorn homology 3-sphere

2016/02/24 by Teruaki Kitano, Kitano, Teruaki, Yoshikazu Yamaguchi +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GN #math.GT

paper · pdf · doi:10.48550/arxiv.1602.07503

openalex publication_date 2016/02/24 · arxiv created 2016/03/03 · arxiv updated 2016/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify SL(2;C)-representations of a Brieskorn homology 3-sphere. We show any irreducible representation into SL(2;C) is conjugate to that into either SU(2) or SL(2;R). We also give a construction of SL(2;R)-representations for a Brieskorn homology 3-sphere from PSL(2;R)-representations of the base orbifold fundamental group.

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