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There are only three known strongly invertible hyperbolic L-space knots with braid index four and tunnel number two. They are t09284 , t10496 and o9_34409 in the SnapPy census. In this paper, we give the first infinite family of strongly invertible hyperbolic L-space knots with braid index four and tunnel number two that includes t10496 and o9_34409 .
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Masakazu Teragaito (2026) studied this question.
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