SU(2)-abelian graph manifolds with a single JSJ torus

2024/08/29 by Giacomo Bascapè, Bascapè, Giacomo
Computer Science · Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Topological and Geometric Data Analysis

paper · doi:10.48550/arxiv.2408.16635

openalex publication_date 2024/08/29 · openalex created_date 2024/10/24 · openalex updated_date 2026/08/04

Abstract

A 3-manifold is called SU(2)-abelian if every SU(2)-representation of its fundamental group has abelian image. We classify, in terms of the Seifert coefficients, SU(2)-abelian 3-manifolds among the family of graph manifolds obtained by gluing two Seifert spaces both fibred over a disk and with two singular fibers. Finally, we prove that these SU(2)-abelian manifolds are Heegaard Floer homology L-spaces.

Related

• Toroidal graph manifolds with small homology are not SU(2)-abelian
• Toroidal homology spheres and SU(2)-representations
• Small Heegaard genus and SU(2)
• Foliations, orders, representations, L-spaces and graph manifolds
• Floer homology on the extended moduli space