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math.GT2026
Boundedness of Dehn surgery slopes admitting hyperbolic -representations for two-bridge knots
Shunjiang Jiang, Ran Tao
We study Dehn fillings on two-bridge knots via non-abelian representations into whose meridian image is hyperbolic. For each fixed nontrivial two-bridg…
math.GT2019
Connected sums of knots do not admit purely cosmetic surgeries
Ran Tao
Two Dehn surgeries on a knot are called purely cosmetic if their surgered manifolds are homeomorphic as oriented manifolds. Gordon conjectured that non-trivial knots in do no…
math.GT2018
Cable knots do not admit cosmetic surgeries
Ran Tao
Two Dehn surgeries on a knot are called purely cosmetic if their surgered manifolds are homeomorphic as oriented manifolds. Gordon conjectured that non-trivial knots in do no…