Sebastian Baader

Scissor equivalence for torus links

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 their signature functions, up to a constant factor.

Positive braids of maximal signature

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 braid links with positive Seifert form and simply laced Dynkin diagrams, as well as a simple classification of alternating positive braid knots.

On the topological 4-genus of torus knots

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 linear estimate of the topological slice genus for torus knots with non-maximal signature invariant.

Legendrian ribbons in overtwisted contact structures

We show that a null-homologous transverse knot K in the complement of an overtwisted disk in a contact 3-manifold is the boundary of a Legendrian ribbon if and only if it possesses a Seifert surface S such that the self-linking number of K with respect to S satisfies

Signature and concordance of positive knots: SIGNATURE AND CONCORDANCE OF POSITIVE KNOTS

\sel(K,S)=-\chi(S)

The volume of positive braid links

. In particular, every null-homologous topological knot type in an overtwisted contact manifold can be represented by the boundary of a Legendrian ribbon. Finally, we show that a contact structure is tight if and only if every Legendrian ribbon minimizes genus in its relative homology class.

Legendrian framings for two-bridge links

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 positive knots.

On the stabilisation height of fibre surfaces in S3

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 Δσ = 2g−σ.

Legendrian graphs and quasipositive diagrams

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 of this paper is a description of the Thurston-Bennequin polytope for two-bridge links. As an application, we construct non-quasipositive surfaces in

Bipartite graphs and combinatorial adjacency

\R^3