Toroidal homology spheres and SU(2)-representations

2021/01/07 by Tye Lidman, Lidman, Tye, Juanita Pinzón‐Caicedo +3 · 1 citation
Mathematics · #57K31 #57M05 #57R58 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2101.02621

openalex publication_date 2021/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that if an integer homology three-sphere contains an embedded incompressible torus, then its fundamental group admits irreducible SU(2)-representations. Our methods use instanton Floer homology, and in particular the surgery exact triangle, holonomy perturbations, and a non-vanishing result due to Kronheimer-Mrowka, as well as results about surgeries on cables due to Gordon.

Citations

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds

Cited by

• SU(2) representations and a large surgery formula

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