English

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

Geometric Topology 2025-09-19 v2

Abstract

We show that if YY is a toroidal closed graph manifold rational homology 33-sphere with H1(Y;Z)5|H_1(Y;\mathbb{Z})| \le 5, then there exists an irreducible representation \fundYSU(2)\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.

Keywords

Cite

@article{arxiv.2506.21729,
  title  = {Toroidal graph manifolds with small homology are not SU(2)-abelian},
  author = {Giacomo Bascape},
  journal= {arXiv preprint arXiv:2506.21729},
  year   = {2025}
}