16 citations · 55 across the 19 of their papers we have counts for
19 papers
A contact version of Kirby's theorem
Marc Kegel, Eric Stenhede, Vera Vértesi
A theorem of Ding and Geiges states that every closed, connected contact -manifold can be obtained from the standard tight contact -sphere by contact -surgery along a…
Khovanov homology of positive links and of L-space knots
Marc Kegel, Naageswaran Manikandan, Leo Mousseau +1
In this article, we develop new obstructions for positivity of links coming from Khovanov homology. More concretely, we show that the first Khovanov homology of a non-split, positi…
Trisecting a 4-dimensional book into three chapters
Marc Kegel, Felix Schmäschke
We describe an algorithm that takes as input an open book decomposition of a closed oriented 4-manifold and outputs an explicit trisection diagram of that 4-manifold. Moreover, a s…
The classification of surfaces via normal curves
Fethi Ayaz, Marc Kegel, Klaus Mohnke
We present a simple proof of the surface classification theorem using normal curves. This proof is analogous to Kneser's and Milnor's proof of the existence and uniqueness of the p…
Non-isotopic transverse tori in Engel manifolds
Marc Kegel
In every Engel manifold we construct an infinite family of pairwise non-isotopic transverse tori that are all smoothly isotopic. To distinguish the transverse tori in the family we…
Census L-space knots are braid positive, except for one that is not
Kenneth L. Baker, Marc Kegel
We exhibit braid positive presentations for all L-space knots in the SnapPy census except one, which is not braid positive. The normalized HOMFLY polynomial of o9_30634, when suita…
Contact surgery graphs
Marc Kegel, Sinem Onaran
We define a graph encoding the structure of contact surgery on contact 3-manifolds and analyze its basic properties and some of its interesting subgraphs.
Contact surgery numbers
John Etnyre, Marc Kegel, Sinem Onaran
It is known that any contact 3-manifold can be obtained by rational contact Dehn surgery along a Legendrian link L in the standard tight contact 3-sphere. We define and study vario…
Stein traces and characterizing slopes
Roger Casals, John Etnyre, Marc Kegel
We show that there exists an infinite family of pairwise non-isotopic Legendrian knots in the standard contact 3-sphere whose Stein traces are equivalent. This is the first example…
A Boothby-Wang theorem for Besse contact manifolds
Marc Kegel, Christian Lange
A Reeb flow on a contact manifold is called Besse if all its orbits are periodic, possibly with different periods. We characterize contact manifolds whose Reeb flows are Besse as p…
Rotation numbers and the Euler class in open books
Sebastian Durst, Marc Kegel, Joan E. Licata
This paper introduces techniques for computing a variety of numerical invariants associated to a Legendrian knot in a contact manifold presented by an open book with a Morse struct…
Handle homology of manifolds
Sebastian Durst, Hansjörg Geiges, Marc Kegel
We give an entirely geometric proof, without recourse to cellular homology, of the fact that in the chain complex defined by a handle decomposition of a given manifo…
Parallelisability of 3-manifolds via surgery
Sebastian Durst, Hansjörg Geiges, Jesús Gonzalo Pérez +1
We present two proofs that all closed, orientable 3-manifolds are parallelisable. Both are based on the Lickorish-Wallace surgery presentation; one proof uses a refinement due to K…
Symplectic dynamics and the 3-sphere
Marc Kegel, Jay Schneider, Kai Zehmisch
Given a knot in a closed connected orientable 3-manifold we prove that if the exterior of the knot admits an aperiodic contact form that is Euclidean near the boundary, then the 3-…
Computing rotation numbers in open books
Sebastian Durst, Marc Kegel
We give explicit formulas and algorithms for the computation of the rotation number of a nullhomologous Legendrian knot on a page of a contact open book. On the way, we derive new…
Cosmetic contact surgeries along transverse knots and the knot complement problem
Marc Kegel
We study cosmetic contact surgeries along transverse knots in the standard contact 3-sphere, i.e. contact surgeries that yield again the standard contact 3-sphere. The main result…
Computing the Thurston-Bennequin invariant in open books
Sebastian Durst, Marc Kegel, Mirko Klukas
We give explicit formulas and algorithms for the computation of the Thurston-Bennequin invariant of a nullhomologous Legendrian knot on a page of a contact open book and on contact…
Computing rotation and self-linking numbers in contact surgery diagrams
Sebastian Durst, Marc Kegel
We give an explicit formula to compute the rotation number of a nullhomologous Legendrian knot in contact (1/n)-surgery diagrams along Legendrian links and obtain a corresponding r…
The Legendrian knot complement problem
Marc Kegel
We prove that every Legendrian knot in the tight contact structure of the 3-sphere is determined by the contactomorphism type of its exterior. Moreover, by giving counterexamples w…