1 citations · 1 across the 8 of their papers we have counts for
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Lens spaces that cannot be obtained by two integral surgeries
Marco Golla, Marc Kegel
In this article, we demonstrate that there exists an infinite family of lens spaces L(p,q) that cannot be obtained from the 3-sphere by two integral surgeries. The first such lens…
Legendrian simple knots not detected by Khovanov homology
Chun-Sheng Hsueh, Marc Kegel, David Suchodoll +1
In this short note, we exhibit a Legendrian simple knot that is not detected by Khovanov homology. This disproves a conjecture of Chernov and Maguire.
The Conway knot has infinite concordance order
Chiara Donatone, Marc Kegel, Lukas Lewark +1
We examine how the Rasmussen invariant, satellite operations, and null-homologous twists can be used to establish infinite order of knots in the smooth concordance group. As an app…
The Unsolvability of the Homeomorphism Problem
Stefan Friedl, Tobias Hirsch, Marc Kegel
In this short expository note, we give a detailed proof of Markov's theorem on the unsolvability of the homeomorphism problem and of the existence of unrecognizable manifolds in al…
Braid positive surgery diagrams
Marc Kegel, Paula Truöl
In this short note, we prove that every closed, oriented, connected 3-manifold arises as Dehn surgery along a braid positive link.
Algorithms in 4-manifold topology
Stefan Bastl, Rhuaidi Burke, Rima Chatterjee +28
We show that there exists an algorithm that takes as input two closed, simply connected, topological 4-manifolds and decides whether or not these 4-manifolds are homeomorphic. In p…
On unknotting fibered positive knots and braids
Marc Kegel, Lukas Lewark, Naageswaran Manikandan +3
The unknotting number and the genus of braid positive knots are equal, as shown by Rudolph. We prove the stronger statement that any positive braid diagram of a genus k…