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INFINITE FAMILIES OF NON-LEFT-ORDERABLE L-SPACES

Abchir, Hamid 大阪大学 DOI:10.18910/89994

2023.01

概要

For each connected alternating tangle, we provide an infinite family of non-left-orderable Lspaces. This gives further support for Conjecture [3] of Boyer, Gordon, and Watson that is a rational homology 3-sphere is an L-space if and only if it is non-left-orderable. These 3-manifolds are obtained as Dehn fillings of the double branched covering of any alternating encircled tangle. We give a presentation of these non-left-orderable L-spaces as double branched coverings of S³, branched over some specified links that turn out to be hyperbolic. We show that the obtained families include many non-Seifert fibered spaces. We also show that these families include many Seifert fibered spaces and give a surgery description for some of them. In the process we give another way to prove that the torus knots T(2, 2m+ 1) are L-space-knots as has already been shown by Ozsváth and Szabó in [24].

参考文献

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