Homology lens spaces and $\mathrm{SL}(2,\mathbb{C})$

Sudipta Ghosh; Steven Sivek; Raphael Zentner

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arXiv · 2509.25019

Homology lens spaces and $\mathrm{SL}(2,\mathbb{C})$

Sudipta Ghosh·Steven Sivek·Raphael Zentner

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Abstract

We prove that if $Y$ is a closed, oriented 3-manifold with first homology $H_1(Y;\mathbb{Z})$ of order less than $5$, then there is an irreducible representation $\pi_1(Y) \to \mathrm{SL}(2,\mathbb{C})$ unless $Y$ is homeomorphic to $S^3$, a lens space, or $\mathbb{RP}^3 \# \mathbb{RP}^3$. By previous work it suffices to consider the case $H_1(Y;\mathbb{Z}) \cong \mathbb{Z}/4\mathbb{Z}$, which we accomplish using holonomy perturbation techniques in instanton Floer homology.

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BibTeX RIS

Sudipta Ghosh, Steven Sivek, Raphael Zentner. 2025-09-29. Homology lens spaces and $\mathrm{SL}(2,\mathbb{C})$. https://arxiv.org/abs/2509.25019

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