5 papers
The search for exotic knot traces
Marc Kegel, Jonathan Spreer
Two distinct knots are said to be friends if their complements, filled along the 0-slope, produce diffeomorphic 3-manifolds. In this article, we develop a practical algorithm, impl…
Complexity of equal 0-surgeries
Tetsuya Abe, Marc Kegel, Nicolas Weiss
We say that two knots are friends if they share the same 0-surgery. Two friends with different sliceness status would provide a counterexample to the 4-dimensional smooth Poincaré…
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…
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…
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…