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

2025/06/26 by Bascape, Giacomo
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2506.21729

Abstract

We show that if Y is a toroidal closed graph manifold rational homology 3-sphere with |H₁(Y;ℤ)| ≤ 5, then there exists an irreducible representation \fundY → 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.

Citations

• Small Heegaard genus and SU(2)
• Order-detection of slopes on the boundaries of knot manifolds
• Slope detection and toroidal 3-manifolds
• Bordered Floer homology for manifolds with torus boundary via immersed curves
• Character varieties of knot complements and branched double-covers via the cord ring
• Foliations, orders, representations, L-spaces and graph manifolds
• The A-polynomial And Holonomy Perturbations
• Knots, sutures and excision
• Dehn surgery, the fundamental group and SU(2)
• Holomorphic disks and three-manifold invariants: properties and applications
• The Geometries of 3-Manifolds

Related

• Toroidal homology spheres and SU(2)-representations
• SU(2)-abelian graph manifolds with a single JSJ torus
• Small Heegaard genus and SU(2)
• A note on surgery obstructions and hyperbolic integer homology spheres
• Determining When The Universal Abelian Cover of a Graph Manifold is a\n Rationla Homology Sphere