相关论文: Open books and plumbings
We introduce a combinatorial model based on measured foliations in surfaces which captures the phenomenology of open/closed string interactions. The predicted equations are derived in this model, and new equations can be discovered as well.…
We show that Brieskorn manifolds with their standard contact structures are contact branched coverings of spheres. This covering maps a contact open book decomposition of the Brieskorn manifold onto a Milnor open book of the sphere.
Euclidean Steiner trees are relevant to model minimal networks in real-world applications ubiquitously. In this paper, we study the feasibility of a hierarchical approach embedded with bundling operations to compute multiple and mutually…
A two-dimensional open book (S,h) determines a closed, oriented three-manifold Y(S,h) and a contact structure C(S,h) on Y(S,h). The contact structure C(S,h) is Stein fillable if h is positive, i.e. h can be written as a product of…
Smale-Barden manifolds are simply-connected closed 5-manifolds. It is an important and difficult question to decide when a Smale-Barden manifold admits a Sasakian or a K-contact structure. The known constructions of Sasakian and K-contact…
Trees with labelled leaves and with all other vertices of degree three play an important role in systematic biology and other areas of classification. A classical combinatorial result ensures that such trees can be uniquely reconstructed…
We classify contact toric 3-manifolds up to contactomorphism, through explicit descriptions, building off of work by Lerman [Lerman03]. As an application, we classify all contact structures on 3-manifolds that can be realised as a concave…
A concept of a rectangular diagram of a foliation in the three-sphere is introduced. It is shown that any co-orientable finite depth foliation in the complement of a link admits a presentation by a rectangular diagram compatible with the…
We study topological open membranes of BF type in a manifest BV formalism. Our main interest is the effect of the bulk deformations on the algebra of boundary operators. This forms a homotopy Lie algebra, which can be understood in terms of…
On a Riemann surface of genus $> 1$, we discuss how to construct opers with apparent singularities from $SL_2(\mathbb{C})$ $\lambda$-connections $(E, \nabla_\lambda)$ and sub-line bundles $L$ of $E$. This construction defines a rational map…
This is the third installment in a series of papers on the subject of derived contact structures. In this paper, we formally introduce the notion of a Legendrian structure in the derived context and provide natural constructions. We then…
We prove that transverse links in any contact manifold $(M,\xi)$ can be realized as a sub-binding of a compatible open book decomposition. We define the support genus of a transverse link and prove that the support genus of a transverse…
We introduce the notion of contact round surgery of index $1$ on Legendrian knots in a general contact 3-manifold. It generalizes the notion of contact round surgery of index 1 on Legendrian knots introduced by Adachi. In…
In this paper, we study strong symplectic fillability and Stein fillability of some tight contact structures on negative parabolic and negative hyperbolic torus bundles over the circle. For the universally tight contact structure with…
We classify fillable contact structures on all negative-definite star-shaped plumbings. Along the way, we show that such Seifert fibred spaces admit a unique negative maximal twisting number, and compute it explicitly using the Alexander…
An isolated complex surface singularity induces a canonical contact structure on its link. In this paper, we initiate the study of the existence problem of Stein cobordisms between these contact structures depending on the properties of…
The purpose of this paper is to introduce Liouville hypersurfaces in contact manifolds, which generalize ribbons of Legendrian graphs and pages of supporting open books. Liouville hypersurfaces are used to define a gluing operation for…
This paper completely answers the question of when contact (r)-surgery on a Legendrian knot in the standard contact structure on the 3-sphere yields a symplectically fillable contact manifold for r in (0,1]. We also give obstructions for…
We show the existence of quasi-cluster $\mathcal{A}$-structures and cluster Poisson structures on moduli stacks of sheaves with singular support in the alternating strand diagram of grid plabic graphs by studying the microlocal parallel…
Twists of contact structures in dimension 3 and higher are studied in this paper from a viewpoint of contact round surgery. Three kinds of new modifications of contact structures which are higher-dimensional generalizations of the…