7 papers · 1 filter
Deciding strong quasipositivity and quasipositivity
Marc Kegel, Qiuyu Ren
We present two results concerning the decidability of (strong) quasipositivity of links in the 3-sphere. First, using a result of Dynnikov--Prasolov, we provide an algorithm to dec…
Trisection invariants of 4-manifolds are uncomputable
Nathan M. Dunfield, Marc Kegel, Shana Yunsheng Li +1
We prove that two invariants of smooth 4-manifolds defined in terms of trisections are uncomputable: the trisection genus and the Kirby-Thompson L-invariant. That is, there does no…
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…
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…