For each nontrivial two-bridge knot, the surgery slopes admitting non-abelian PSL(2,R) representations with hyperbolic meridian are bounded.
Teragaito, Left-orderability and exceptional Dehn surgery on twist knots, Canad
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Boundedness of Dehn surgery slopes admitting hyperbolic $\mathrm{PSL}(2,\mathbb{R})$-representations for two-bridge knots
For each nontrivial two-bridge knot, the surgery slopes admitting non-abelian PSL(2,R) representations with hyperbolic meridian are bounded.