Heegaard Floer homology, L-spaces and smoothing order on links II

TL;DR

This paper classifies certain L-spaces with vanishing boundary maps in Heegaard Floer homology, using the smoothing order on links, extending previous systematic collection to a classification under specific constraints.

Contribution

It provides a classification of L-spaces with vanishing boundary maps based on the smoothing order on links, advancing the understanding of their structure.

Findings

Classified L-spaces with vanishing boundary maps under specific constraints

Extended previous systematic collection to a classification result

Deepened understanding of the relationship between links and L-spaces

Abstract

We focus on L-spaces for which the boundary maps of the Heegaard Floer chain complexes vanish. In previous paper \cite{Usui}, we collect such manifolds systematically by using the smoothing order on links. In this paper, we classify such L-spaces under appropreate constraint.