Genus one open books with non-left-orderable fundamental group
Yu Li, Liam Watson

TL;DR
This paper proves that for certain genus one open book decompositions of three-manifolds, being an L-space implies the fundamental group is not left-orderable, addressing a question in 3-manifold topology.
Contribution
It establishes a link between L-space property and non-left-orderability of the fundamental group for genus one open books, answering a previously open question.
Findings
L-space manifolds with genus one open books have non-left-orderable fundamental groups.
The result confirms a conjecture relating L-spaces and orderability in this class.
Provides new insights into the structure of 3-manifolds with genus one open books.
Abstract
Let be a closed, connected, orientable three-manifold admitting a genus one open book decomposition with one boundary component. We prove that if is an L-space, then the fundamental group of is not left-orderable. This answers a question posed by John Baldwin.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology
