English

Toroidal homology spheres and SU(2)-representations

Geometric Topology 2021-01-08 v1

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.

Keywords

Cite

@article{arxiv.2101.02621,
  title  = {Toroidal homology spheres and SU(2)-representations},
  author = {Tye Lidman and Juanita Pinzón-Caicedo and Raphael Zentner},
  journal= {arXiv preprint arXiv:2101.02621},
  year   = {2021}
}

Comments

26 pages, 5 figures