相关论文: Open books and plumbings

Let $\Lambda$ be a closed, connected, spin Legendrian submanifold of the 1-jet space of a smooth $n$-dimensional manifold. We give a coherent orientation scheme for the moduli space of rigid Morse flow trees of $\Lambda$, implying that the…

A flat plumbing basket is a surface consisting a disk and finitely many bands which are contained in distinct pages of the trivial open book decomposition of $\mathbf{S}^{3}$. In this paper, we construct a Legendrian link from a flat…

Given an open book decomposition of a contact three man-ifold (M, $\xi$) with pseudo-Anosov monodromy and fractional Dehn twist coefficient c = k n, we construct a Legendrian knot $\Lambda$ close to the stable foliation of a page, together…

We prove that for any contact 3-manifold supported by a spinal open book decomposition with planar pages, there is a universal bound on the Euler characteristic and signature of its minimal symplectic fillings. The proof is an application…

Let $Y$ be a closed, connected, orientable three-manifold admitting a genus one open book decomposition with one boundary component. We prove that if $Y$ is an L-space, then the fundamental group of $Y$ is not left-orderable. This answers a…

By recent results of Baker--Etnyre--Van Horn-Morris, a rational open book decomposition defines a compatible contact structure. We show that the Heegaard Floer contact invariant of such a contact structure can be computed in terms of the…

A strongly non-degenerate mixed function has a Milnor open book structures on a sufficiently small sphere. We introduce the notion of {\em a holomorphic-like} mixed function and we will show that a link defined by such a mixed function has…

It is known that there are surface bundles of arbitrarily high genus which have genus two Heegaard splittings. The simplest examples are Seifert fibered spaces with the sphere as a base space, three exceptional fibers and which allow…

In this note we make several observations concerning symplectic fillings. In particular we show that a (strongly or weakly) semi-fillable contact structure is fillable and any filling embeds as a symplectic domain in a closed symplectic…

In this paper, we show that any topological knot or link in $S^1 \times S^2$ sits on a planar page of an open book decomposition whose monodromy is a product of positive Dehn twists. As a consequence, any knot or link type in $S^1 \times…

We say that a contact manifold is Milnor fillable if it is contactomorphic to the contact boundary of an isolated complex-analytic singularity (X,x). Generalizing results of Milnor and Giroux, we associate to each holomorphic function f…

We show that two open books in a given closed, oriented three-manifold admit isotopic stabilizations, where the stabilization is made by successive plumbings with Hopf bands, if and only if their associated plane fields are homologous.…

We study homotopically non-trivial spheres of Legendrians in the standard contact R3 and S3. We prove that there is a homotopy injection of the contactomorphism group of S3 into some connected components of the space of Legendrians induced…

It is shown that the number of pages required for a book embedding of a graph is the maximum of the numbers needed for any of the maximal nonseparable subgraphs and that a plane graph in which every triangle bounds a face has a two-page…

We introduce a new Legendrian isotopy invariant for any closed orientable Legendrian surface $L$ embedded in a closed contact $5$-manifold $(M, \xi)$ which admits an "admissable" open book $(B, f)$ (supporting $\xi$) for $L$. We show that…

We give an algorithm which produces infinitely many pairwise exotic Stein fillings of the same contact 3-manifolds, applying positive allowable Lefschetz fibrations over the disk. As a corollary, for a large class of Stein fillings, we…

We describe the Stein handlebody diagrams of Milnor fibers of Brieskorn singularities $x^p + y^q + z^r = 0$. We also study the natural symplectic operation by exchanging two Stein fillings of the canonical contact structure on the links in…

In the paper arXiv:0810.4291 we have shown, in the context of type II superstring theory, the classification of the allowed B-field and A-field configurations in the presence of anomaly-free D-branes, the mathematical framework being…

Lagrangian cobordisms between Legendrian knots arise in Symplectic Field Theory and impose an interesting and not well-understood relation on Legendrian knots. There are some known "elementary" building blocks for Lagrangian cobordisms that…

For a nullhomologous Legendrian knot in a closed contact 3-manifold Y we consider a contact structure obtained by positive rational contact surgery. We prove that in this situation the Heegaard Floer contact invariant of Y is mapped by a…