L-space intervals for Graph Manifolds and Cables

TL;DR

This paper extends the classification of L-space intervals to graph manifolds and cables, providing recursive formulas and applications to Floer simple manifolds, enhancing understanding of L-space fillings in 3-manifold topology.

Contribution

It introduces a finite recursive formula for L-space intervals in graph manifolds and generalizes this to cables of Floer simple knot complements, connecting to existing results.

Findings

Finite recursive formula for L-space intervals in graph manifolds

Explicit computation of L-space intervals for cable knots

Recovery of Hedden and Hom's results as a special case

Abstract

We present a graph manifold analog of the Jankins-Neumann classification of Seifert fibered spaces over $S^2$ admitting taut foliations, providing a finite recursive formula to compute the L-space Dehn-filling interval for any graph manifold with torus boundary. As an application of a generalization of this result to Floer simple manifolds, we compute the L-space interval for any cable of a Floer simple knot complement in a closed three-manifold in terms of the original L-space interval, recovering a result of Hedden and Hom as a special case.