Related papers: Nonexistence and existence of fillable contact str…
We show the existence of tight contact structures on infinitely many hyperbolic three-manifolds obtained via Dehn surgeries along sections of hyperbolic surface bundles over circle.
This is a survey on contact open books and contact Dehn surgery. The relation between these two concepts is discussed, and various applications are sketched, e.g. the monodromy of Stein fillable contact 3-manifolds, the Giroux-Goodman proof…
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 various versions of contact surgery numbers, the minimal number…
In this paper, we find infinite hyperbolic 3-manifolds that admit no weakly symplectically fillable contact structures, using tools in Heegaard Floer theory. We also remark that part of these manifolds do admit tight contact structures.
We classify all the non-hyperbolic Dehn fillings of the complement of the chain-link with 3 components, conjectured to be the smallest hyperbolic 3-manifold with 3 cusps. We deduce the classification of all non-hyperbolic Dehn fillings of…
We show that there are vast families of contact 3-manifolds each member of which admits infinitely many Stein fillings with arbitrarily big euler characteristics and arbitrarily small signatures ---which disproves a conjecture of Stipsicz…
We show that for all $n \ge 3$, any $(2n+1)$-dimensional manifold that admits a tight contact structure, also admits a tight but non-fillable contact structure, in the same almost contact class. For $n=2$, we obtain the same result,…
Infinitely many contact 3-manifolds each admitting infinitely many, pairwise non-diffeomorphic Stein fillings are constructed. We use Lefschetz fibrations in our constructions and compute their first homologies to distinguish the fillings.
In this note we will determine which contact structures on manifolds obtained by certain surgeries on the right handed trefoil are Stein fillable and which are not. This continues a long line of research and shows that there seems to be few…
We continue our study of contact structures on manifolds of dimension at least five using complex surgery theory. We show that in each dimension 2q+1 > 3 there are 'maximal' almost contact manifolds to which there is a Stein cobordism from…
We show that, for any given 3-manifold M, there are at most finitely many hyperbolic knots K in the 3-sphere and fractions p/q (with q > 22), such that M is obtained by p/q surgery along K. This is a corollary of the following result. If M…
In this note, we classify Stein fillings of an infinite family of contact 3-manifolds up to diffeomorphism. Some contact 3-manifolds in this family can be obtained by Legendrian surgeries on $(S^3,\xi_{std})$ along certain Legendrian…
We exhibit tight contact structures on 3-manifolds that do not admit any symplectic fillings.
The aim of this paper is to demonstrate that very many Dehn fillings on a cusped hyperbolic 3-manifold yield a 3-manifold which is irreducible, atoroidal and not Seifert fibred, and which has infinite, word hyperbolic fundamental group. We…
In this paper we discuss a general strategy to detect the absence of weakly symplectic fillings of $L$-spaces. We start from a generic $L$-space knot and consider (positive) Dehn surgeries on it. We compute, using arithmetic data depending…
A geometric obstruction, the so called "plastikstufe", for a contact structure to not being fillable has been found by K. Niederkruger. This generalizes somehow the concept of overtwisted structure to dimensions higher than 3. This paper…
A spinal open book decomposition on a contact manifold is a generalization of a supporting open book which exists naturally e.g. on the boundary of a symplectic filling with a Lefschetz fibration over any compact oriented surface with…
This paper concerns the Dehn surgery construction, especially those Dehn surgeries leaving the manifold unchanged. In particular, we describe an oriented 1-cusped hyperbolic 3-manifold X with a pair of slopes r_1, r_2 such that the Dehn…
These are notes of a talk given at the Mathematische Arbeitstagung 2005 in Bonn. Following ideas of Ozbagci-Stipsicz, a proof based on contact Dehn surgery is given of Eliashberg's concave filling theorem for contact 3-manifolds. The role…
We give a bordism-theoretic characterisation of those closed almost contact (2q+1)-manifolds (with q > 2) which admit a Stein fillable contact structure. Our method is to apply Eliashberg's h-principle for Stein manifolds in the setting of…