Strong L-spaces and left orderability

TL;DR

This paper introduces strong L-spaces, a class of rational homology 3-spheres with computable Heegaard Floer homology, and proves their fundamental groups are not left-orderable, with examples from double branched covers of alternating links.

Contribution

It defines the new concept of strong L-spaces and establishes a link between their Floer homology and the non-left-orderability of their fundamental groups.

Findings

Strong L-spaces have computable chain-level Heegaard Floer homology.

Fundamental groups of strong L-spaces are not left-orderable.

Examples include double branched covers of alternating links.

Abstract

We introduce the notion of a strong L-space, a closed, oriented rational homology 3-sphere whose Heegaard Floer homology can be determined at the chain level. We prove that the fundamental group of a strong L-space is not left-orderable. Examples of strong L-spaces include the double branched covers of alternating links in S^3.