2015/10/08 by Steven Boyer, Adam Clay, Boyer, Steven +1
Computer Science · Mathematics · #57M25 #57M50 #57M99 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1510.02378
openalex publication_date 2015/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A graph manifold rational homology 3-sphere W with a left-orderable fundamental group admits a co-oriented taut foliation, though it is unknown whether it admits a smooth co-oriented taut foliation. In this paper we extend the gluing theorem of arXiv:1401.7726 to graph manifold rational homology solid tori and use this to show that there are smooth foliations on the pieces of W which come close to matching up on its JSJ tori. This is applied to prove that a graph manifold with left-orderable fundamental group is not an L-space.