Geometry and Topology Seminar - Idrissa Ba - Circular orderability of 3-manifold groups
Title: Circular orderability of 3-manifold groups.
Speaker: Idrissa Ba (University of Manitoba)
Abstract: It was conjectured by Boyer-Gordon-Watson, given an irreducible rational homology 3-sphere $M$, the fact that the fundamental group of $M$ is left orderable is equivalent to the fact that $M$ is not an L-space. Since the set of left orderings of $\pi_1(M)$ is a subset of the set of circularly orderings of $\pi_1(M)$, it is natural to ask the relationship between $M$ being anL-space and $\pi_1(M)$ being circularly orderable. We study this question and we show that the fundamental group of any compact, connected Seifert fibred space $M$ is circularly orderable if and only if it is infinite or finite cyclic. We also study the circularly orderability of the fundamental group of graph manifolds.
We also show that the fundamental group of a compact, connected Sol manifold is circularly orderable.
We give examples of3-manifolds with non-circularly orderable fundamental groups as double branched cover of links (alternating links and non-alternating quasi-alternating links). This is joint work with Adam Clay.
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