Guts of nearly fibered knots

TL;DR

This paper provides models for the guts of nearly fibered knots, showing that their nearly fibered condition can be characterized topologically and is independent of Floer theory specifics.

Contribution

It introduces three models for the guts of nearly fibered knots and establishes a topological characterization of the nearly fibered condition.

Findings

Three models for the guts of nearly fibered knots are provided.

The nearly fibered condition is shown to be topologically characterizable.

The nearly fibered property is independent of Floer theory variations.

Abstract

The guts of a knot is an invariant defined for the knot complement by Agol-Zhang. Nearly fibered knots, which are defined as knots whose Floer homology has dimension two in the top Alexander grading, were introduced by Baldwin-Sivek. In this note, we provide three models for the guts of nearly fibered knots in the $3$-sphere. As a corollary, the nearly fibered condition can be purely topologically characterized and is independent of the specific version of Floer theory.