Toroidal homology spheres and SU(2)-representations

Tye Lidman; Juanita Pinzón-Caicedo; Raphael Zentner

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arXiv · 2101.02621

Toroidal homology spheres and SU(2)-representations

Tye Lidman·Juanita Pinzón-Caicedo·Raphael Zentner

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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.

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BibTeX RIS

Tye Lidman, Juanita Pinzón-Caicedo, Raphael Zentner. 2021-01-07. Toroidal homology spheres and SU(2)-representations. https://arxiv.org/abs/2101.02621

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