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

TL;DR

This paper investigates L-spaces with vanishing boundary maps in Heegaard Floer homology, systematically classifying them using the smoothing order on links to understand their structure.

Contribution

It introduces a systematic approach to classify certain L-spaces via the smoothing order on links, expanding understanding of their properties.

Findings

Identification of a class of L-spaces with vanishing boundary maps

Systematic collection of such manifolds using smoothing order

Enhanced understanding of the structure of these L-spaces

Abstract

In this paper, we focus on L-spaces for which the boundary maps of the Heegaard Floer chain complexes vanish. We collect such manifolds systematically by using the smoothing order on links.