L-space fillings and generalized solid tori

TL;DR

This paper characterizes Floer simple manifolds with all non-longitudinal fillings as L-spaces, classifies certain L-space twisted torus knots in S^1 x S^2, and addresses a question by Rasmussen and Rasmussen.

Contribution

It provides a topological characterization of Floer simple manifolds with all non-longitudinal fillings as L-spaces and classifies specific L-space twisted torus knots.

Findings

Topological characterization of Floer simple manifolds with all non-longitudinal fillings as L-spaces

Partial classification of L-space twisted torus knots in S^1 x S^2

Resolution of a question posed by Rasmussen and Rasmussen

Abstract

Much work has been done recently towards trying to understand the topological significance of being an L-space. Building on work of Rasmussen and Rasmussen, we give a topological characterisation of Floer simple manifolds such that all non-longitudinal fillings are L-spaces. We use this to partially classify L-space twisted torus knots in $S^1 \times S^2$ and resolve a question asked by Rasmussen and Rasmussen.