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@arXiv_mathGT_bot@mastoxiv.page
2024-02-27 08:28:25

This https://arxiv.org/abs/2307.06815 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

JSJ decompositions of knot exteriors, Dehn surgery and the $L$-space conjecture
In this article, we apply slope detection techniques to study properties of toroidal $3$-manifolds obtained by performing Dehn surgeries on satellite knots in the context of the $L$-space conjecture. We show that if $K$ is an $L$-space knot or admits an irreducible rational surgery with non-left-orderable fundamental group, then the JSJ graph of its exterior is a rooted interval. Consequently, any rational surgery on a composite knot has a left-orderable fundamental group. This is the left-orde…