Large embedded balls and Heegaard genus in negative curvature.
Legendrian and transverse twist knots
In 1997, Chekanov gave the first example of a Legendrian nonsimple knot type: the knot. Epstein, Fuchs, and Meyer extended his result by showing that there are at least different Legendrian representatives with maximal Thurston-Bennequin number of the twist knot with crossing number . In this paper we give a complete classification of Legendrian and transverse representatives of twist knots. In particular, we show that has exactly Legendrian representatives with maximal Thurston–Bennequin...
Legendrian knots and monopoles.
Les invariants des 3-variétés périodiques
Soit un entier . Une 3-variété est dite -périodique si et seulement si le groupe cyclique agit semi-librement sur avec un cercle comme l’ensemble des points fixes. Dans cet article, nous utilisons les invariants quantiques pour établir des conditions nécessaires pour qu’une 3-variété soit périodique.
Levelling an unknotting tunnel.
Link concordance, homology cobordism, and Hirzebruch-type defects from iterated p-covers
Link homology and Frobenius extensions
We explain how rank two Frobenius extensions of commutative rings lead to link homology theories and discuss relations between these theories, Bar-Natan theories, equivariant cohomology and the Rasmussen invariant.
Link invariants from finite biracks
A birack is an algebraic structure with axioms encoding the blackboard-framed Reidemeister moves, incorporating quandles, racks, strong biquandles and semiquandles as special cases. In this paper we extend the counting invariant for finite racks to the case of finite biracks. We introduce a family of biracks generalizing Alexander quandles, (t,s)-racks, Alexander biquandles and Silver-Williams switches, known as (τ,σ,ρ)-biracks. We consider enhancements of the counting invariant using writhe vectors,...
Link invariants from finite racks
We define ambient isotopy invariants of oriented knots and links using the counting invariants of framed links defined by finite racks. These invariants reduce to the usual quandle counting invariant when the rack in question is a quandle. We are able to further enhance these counting invariants with 2-cocycles from the coloring rack's second rack cohomology satisfying a new degeneracy condition which reduces to the usual case for quandles.
Links and cycles II: families of commutation relations, parametrized by knots, in the mapping class groups and beyond
We generate families of commutation relations in various groups, by examining quandle colorings of knots and their quandle 2-cycles. The colorings are via quandles associated to the given groups.
Links associated with generic immersions of graphs.
Löbell manifolds revised.
Locally unknotted spines of Heegaard splittings.
Longitude Floer homology and the Whitehead double.