Corpus ID: 230799466

Toroidal homology spheres and SU(2)-representations

@inproceedings{Lidman2021ToroidalHS,
  title={Toroidal homology spheres and SU(2)-representations},
  author={Tye Lidman and Juanita Pinz'on-Caicedo and Raphael Zentner},
  year={2021}
}
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. 
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