Genus one open books with non-left-orderable fundamental group

Abstract

Let $Y$ be a closed, connected, orientable three-manifold admitting a genus one open book decomposition with one boundary component. We prove that if $Y$ is an L-space, then the fundamental group of $Y$ is not left-orderable. This answers a question posed by John Baldwin.

10 pages, 3 figures

References in corpus (3)

• On L-spaces and non left-orderable 3-manifold groups
• Non-left-orderable double branched coverings
• On L-spaces and left-orderable fundamental groups