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

2011/09/22 by Yu Li, Liam Watson, Li, Yu +1
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT

paper · pdf · doi:10.48550/arxiv.1109.4870

10 pages, 3 figures

arxiv created 2011/09/22 · openalex publication_date 2011/09/22 · arxiv updated 2011/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The Geometries of 3-Manifolds

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