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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
An algorithm for finding minimal volume hyperbolic links and the Dehn parental test
Misha Schmalian
We describe an algorithm that, given a 3-manifold M, outputs a finite set containing all minimal volume k-component hyperbolic link complements in M. A key step, that might be of i…