Publications (51)
3-braid knots with maximal 4-genus
Sebastian Baader, Lukas Lewark, Filip Misev +1
We classify 3-braid knots whose topological 4-genus coincides with their Seifert genus, using McCoy's twisting method and the Xu normal form. In addition, we give upper bounds for…
Moebius bands with a quasipositive fibred hole
Sebastian Baader
We prove that every knot in the 3-space bounds an embedded punctured Moebius band whose other boundary component is a quasipositive fibred knot.
Trefoil Plumbing
Sebastian Baader, Pierre Dehornoy
We give a criterion for an open book to contain an n-times iterated Hopf plumbing summand. As an application, we show that fibre surfaces of positive braid knots admit a trefoil pl…
Unknotting sequences for torus knots
Sebastian Baader
The unknotting number of a knot is bounded from below by its slice genus. It is a well-known fact that the genera and unknotting numbers of torus knots coincide. In this note we ch…
Systoles on punctured spheres
Sebastian Baader, Jasmin Jörg
We determine the maximal number of systoles among all spheres with punctures endowed with a complete Riemannian metric of finite area.
Secondary Braid Groups
Sebastian Baader, Michael Lönne
We generalize presentations of the fundamental group of discriminant complements and arrive at a class of presentations associated naturally with words in the free monoid of the al…
The stable 4-genus of alternating knots
Sebastian Baader, Lukas Lewark
We show that the difference between the genus and the stable topological 4-genus of alternating knots is either zero or at least 1/3.
On the stable 4-genus of knots with indefinite Seifert form
Sebastian Baader
Under a simple assumption on Seifert surfaces, we characterise knots whose stable topological 4-genus coincides with the genus.
Khovanov width and dealternation number of positive braid links
Sebastian Baader, Peter Feller, Lukas Lewark +1
We give asymptotically sharp upper bounds for the Khovanov width and the dealternation number of positive braid links, in terms of their crossing number. The same braid-theoretic t…
Coxeter groups and meridional rank of links
Sebastian Baader, Ryan Blair, Alexandra Kjuchukova
We prove the meridional rank conjecture for twisted links and arborescent links associated to bipartite trees with even weights. These links are substantial generalizations of pret…
Trefoils and hexafoils in 3-braids
Sebastian Baader, Levi Ryffel
We determine the cobordism distance between all positive 3-braid links and connected sums of trefoil knots, up to a constant error. This may be seen as a reinterpretation of Coxete…
On the stabilisation height of fibre surfaces in
Sebastian Baader, Filip Misev
The stabilisation height of a fibre surface in the 3-sphere is the minimal number of Hopf plumbing operations needed to attain a stable fibre surface from the initial surface. We s…
Asymptotic Rasmussen Invariant
Sebastian Baader
We use simple properties of the Rasmussen invariant of knots to study its asymptotic behaviour on the orbits of a smooth volume preserving vector field on a compact domain in the 3…
Minor theory for quasipositive surfaces
Sebastian Baader, Pierre Dehornoy, Livio Liechti
The set of quasipositive surfaces is closed under incompressible inclusion. We prove that the induced order on fibre surfaces of positive braid links is almost a well-quasi-order.…
A note on Vassiliev invariants of quasipositive knots
Sebastian Baader
It has been known that any Alexander polynomial of a knot can be realized by a quasipositive knot. As a consequence, the Alexander polynomial cannot detect quasipositivity. In this…
Pushing the Performance Limits in Autonomous Racing: Continuous Stability-Aware Adaptive Velocity Planning in Formula Student Driverless
Tamara Bergerhoff, Sebastian Baader, Pascal MeiÃner +1
In autonomous racing, especially in competitions such as Formula Student Driverless, precise planning of the target velocity of a race car is crucial for competitive lap times and…
Asymptotics of the smooth -realization problem
Sebastian Baader, Peter Feller
We solve an asymptotic variant of a smooth version of the -realization problem for plane curves. As an application, we determine the cobordism distance between torus links of…
Minimal cobordisms between thin and thick torus knots
Sebastian Baader, Lukas Lewark, Filip Misev +1
We determine the locally flat cobordism distance between torus knots with small and large braid index, up to high precision. Here small means 2, 3, 4, or 6. As an application, we d…
Minor theory for surfaces and divides of maximal signature
Sebastian Baader, Pierre Dehornoy
The paper is partially withdrawn: in its current form, Lemma 2.3 is false, so that our proof of Theorem A and Proposition B has an important gap. We were unable to fix it yet. Any…
Positive braids of maximal signature
Sebastian Baader
We characterise positive braid links with positive Seifert form via a finite number of forbidden minors. From this we deduce a one-to-one correspondence between prime positive brai…
Asymptotic link invariants for ergodic vector fields
Sebastian Baader
We study the asymptotics of a family of link invariants on the orbits of a smooth volume-preserving ergodic vector field on a compact domain of the 3-space. These invariants, calle…
Arborescence of positive Thompson links
Valeriano Aiello, Sebastian Baader
We show that the links associated with positive elements of the Thompson group coincide with the closures of bipartite arborescent tangles.
Vehicle Prediction Model for Enhanced MPC Path Tracking in Formula Student Driverless
Sebastian Baader, Tamara Bergerhoff, Pascal MeiÃner +1
Autonomous race cars, such as in Formula Student Driverless, operate close to their physical handling limits. The resulting highly nonlinear vehicle behavior increases the path tra…
On the crossing number of arithmetic curve systems
Sebastian Baader, Claire Burrin, Luca Studer
We show that the family of systoles of hyperbolic surfaces associated with congruence lattices in have asymptotically minimal crossing number.
The volume of positive braid links
Sebastian Baader
Based on recent work by Futer, Kalfagianni and Purcell, we prove that the volume of sufficiently complicated positive braid links is proportional to the signature defect $ÎÏ=2g-Ï…
Signature spectrum of positive braids
Sebastian Baader
We derive a lower bound for all Levine-Tristram signatures of positive braid links, linear in terms of the first Betti number. As a consequence, we obtain upper and lower bounds on…
Asymptotic Vassiliev Invariants for Vector Fields
Sebastian Baader, Julien Marche
We analyse the asymptotical growth of Vassiliev invariants on non-periodic flow lines of ergodic vector fields on domains of . More precisely, we show that the asymptotics of…
Slice and Gordian numbers of track knots
Sebastian Baader
We present a class of knots associated with labelled generic immersions of intervals into the plane and compute their Gordian numbers and 4-dimensional invariants. At least 10% of…
Legendrian graphs and quasipositive diagrams
Sebastian Baader, Masaharu Ishikawa
In this paper we clarify the relationship between ribbon surfaces of Legendrian graphs and quasipositive diagrams by using certain fence diagrams. As an application, we give an alt…
Symmetric quotients of knot groups and a filtration of the Gordian graph
Sebastian Baader, Alexandra Kjuchukova
We define a metric filtration of the Gordian graph by an infinite family of 1-dense subgraphs. The n-th subgraph of this family is generated by all knots whose fundamental groups s…
Positive oriented Thompson links
Valeriano Aiello, Sebastian Baader
We prove that the links associated with positive elements of the oriented subgroup of the Thompson group are positive.
Signature and concordance of positive knots
Sebastian Baader, Pierre Dehornoy, Livio Liechti
We derive a linear estimate of the signature of positive knots, in terms of their genus. As an application, we show that every knot concordance class contains at most finitely many…
Monomial reduction of knot polynomials
Sebastian Baader
For all natural numbers and prime numbers , we find a knot whose skein polynomial evaluated at has trivial reduction modulo . An interesting conseque…
The crossing number of polynomial curve systems
Sebastian Baader, Jasmin Jörg, Hugo Parlier
We determine the crossing number of polynomial size curve systems on standard surfaces, in terms of the genus, up to high precision.
Ãtude on the Delta-unknotting number
Sebastian Baader, Lukas Lewark
We derive an almost sharp lower bound on the Casson invariant of positive braid knots. As a consequence, we show that the -unknotting number is quasi-additive on the set of pos…
Two strand twisting
Lambert A'Campo, Sebastian Baader, Livio Ferretti +1
We prove that fibred knots cannot be untied with -moves, for all . More generally, we give an upper bound on the number of two strand twist operations that…
Average four-genus of two-bridge knots
Sebastian Baader, Alexandra Kjuchukova, Lukas Lewark +2
We prove that the expected value of the ratio between the smooth four-genus and the Seifert genus of two-bridge knots tends to zero as the crossing number tends to infinity.
On the Jones polynomial modulo primes
Valeriano Aiello, Sebastian Baader, Livio Ferretti
We derive an upper bound on the density of Jones polynomials of knots modulo a prime number , within a sufficiently large degree range: . As an application, we classify k…
Bipartite graphs and combinatorial adjacency
Sebastian Baader
We present a simple combinatorial model for quasipositive surfaces and positive braids, based on embedded bipartite graphs. As a first application, we extend the well-known duality…
Combinatorial cusp count and clover invariants
Sebastian Baader, Masaharu Ishikawa
We construct efficient topological cobordisms between torus links and large connected sums of trefoil knots. As an application, we show that the signature invariant at $Ï=…
Bouquets of curves in surfaces
Sebastian Baader, Peter Feller, Levi Ryffel
We characterise when a set of simple closed curves in an orientable surface forms a bouquet, in terms of relations between the corresponding Dehn twists.
On the topological 4-genus of torus knots
Sebastian Baader, Peter Feller, Lukas Lewark +1
We prove that the topological locally flat slice genus of large torus knots takes up less than three quarters of the ordinary genus. As an application, we derive the best possible…
Gordian distance and Vassiliev invariants
Sebastian Baader
The Gordian distance between two knots measures how many crossing changes are needed to transform one knot into the other. It is known that there are always infinitely many non-equ…
Scissor equivalence for torus links
Sebastian Baader
This article is about a natural distance function induced by smooth cobordisms between links. We show that the cobordism distance of torus links is determined by the profiles of th…
Untwisting 3-strand torus knots
Sebastian Baader, Ian Banfield, Lukas Lewark
We prove that the signature bound for the topological 4-genus of 3-strand torus knots is sharp, using McCoy's twisting method. We also show that the bound is off by at most 1 for 4…
Sparse curve systems have intermediate growth type
Sebastian Baader, Jasmin Jörg, Danica KosanoviÄ
A system of simple closed curves on a surface of genus is said to be sparse if their average pairwise intersection number does not exceed one. We show that the maximal size of…
Checkerboard graph monodromies
Sebastian Baader, Lukas Lewark, Livio Liechti
We associate an open book with any connected plane checkerboard graph, thus providing a common extension of the classes of prime positive braid links and positive tree-like Hopf pl…
Construction of non-alternating knots
Sebastian Baader
We investigate the behaviour of Rasmussen's invariant under the sharp operation on knots and obtain a lower bound for the sharp unknotting number. This bound leads us to an int…
The bridge number of arborescent links with many twigs
Sebastian Baader, Ryan Blair, Alexandra Kjuchukova +1
We prove the meridional rank conjecture for arborescent links associated to plane trees with the following property: all branching points carry a straight branch to at least three…
Legendrian framings for two-bridge links
Sebastian Baader, Masaharu Ishikawa
We define the Thurston-Bennequin polytope of a two-component link as the convex hull of all pairs of integers that arise as framings of a Legendrian representative. The main result…
Distortion of spheres and surfaces in space
Sebastian Baader, Luca Studer, Roger Züst
It is known that the surface of a cone over the unit disc with large height has smaller distortion than the standard embedding of the 2-sphere in . In this note we sho…