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