Detecting Heegaard Floer homology solid tori

TL;DR

This paper characterizes Heegaard Floer homology solid tori by their Dehn fillings, providing a criterion involving non-separating 2-spheres, and classifies Seifert fibered cases.

Contribution

It establishes a new characterization of Heegaard Floer homology solid tori based on Dehn filling properties and classifies Seifert fibered instances.

Findings

A rational homology solid torus is a Heegaard Floer homology solid torus iff it admits a Dehn filling with a non-separating 2-sphere.

Seifert fibered Heegaard Floer solid tori are explicitly characterized.

The paper provides a criterion linking Dehn fillings and Floer homology properties.

Abstract

We show that a rational homology solid torus is a Heegaard Floer homology solid torus if and only if it has a Dehn filling with a non-separating 2-sphere. Using this, we characterize Seifert fibered Heegaard Floer solid tori.