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math.GT2025
Links have no characterising slopes
Marc Kegel, Misha Schmalian
We show that there is no analogue of characterising slopes for multi-component links. Concretely, we show that for any ordered link L in S3 with n>1 components and any rational slo…
math.GT2025
Unique Surgery Descriptions along Knots
Marc Kegel, Misha Schmalian
We prove that for any non-trivial knot K, infinitely many r-surgeries K(r) along K have a unique surgery description along a knot. Moreover, we show that for any hyperbolic L-space…
math.GT2025
Knots that share four surgeries
Marc Kegel, Lisa Piccirillo
Distinct knots K, K' can sometimes share a common p/q-framed Dehn surgery. A folk conjecture held that for a fixed pair of knots, this can occur for at most one value of p/q. We di…