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arXiv · 2506.21729

Toroidal graph manifolds with small homology are not SU(2)-abelian

Giacomo Bascape
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Abstract

We show that if $Y$ is a toroidal closed graph manifold rational homology $3$-sphere with $|H_1(Y;\mathbb{Z})| \le 5$, then there exists an irreducible representation $\fund{Y} \to SU(2)$, using topological methods and avoiding the use of gauge theory. This answers positively to a conjecture by Baldwin and Sivek in the case of graph manifolds.

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Giacomo Bascape. 2025-09-17. Toroidal graph manifolds with small homology are not SU(2)-abelian. https://arxiv.org/abs/2506.21729

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