Strong L-spaces and left orderability

2011/10/04 by Adam Simon Levine, Sam Lewallen · 1 citation
Mathematics · #math.GT #msc:20F60 #msc:57M05 #msc:57R58

paper · pdf

published as Mathematical Research Letters 19 (2012), no. 6, 1237-1244 · 9 pages

arxiv created 2011/10/04 · arxiv updated 2014/05/02

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 S³.

Cited by

• The next-to-top term of the knot Floer homology of some non-fibered knots

Related

• On left-orderability and double branched covers of Kanenobu's knots
• On L-spaces and left-orderable fundamental groups
• On L-spaces and non left-orderable 3-manifold groups
• Infinite families of non-left-orderable L-spaces
• Foliations, orders, representations, L-spaces and graph manifolds