Related papers: On open books and embedding of smooth and contact …

We discuss $4$-dimensional achiral Lefschetz fibrations bounding $3$-dimensional open books and study their Lefschetz fibration (LF) embedding in a bounded $6$-dimensional manifold, in the sense of Ghanwat--Pancholi. As an application we…

We prove some open book embedding results in the contact category. For example, we show that a large class of contact 3-manifolds admit contact open book embedding in the standard contact 5- sphere. We also prove that all the Ustilovsky (4m…

In this paper, we prove Lefschetz fibration embeddings of achiral as well as simplified broken (achiral) Lefschetz fibrations of compact, connected, orientable $4$-manifolds over $D^2$ into the trivial Lefschetz fibration of $\mathbb…

In this paper, we introduce the notions of an iterated planar Lefschetz fibration and an iterated planar open book decomposition and prove the Weinstein conjecture for contact manifolds supporting an open book that has iterated planar…

We prove some contact analogs of smooth embedding theorems for closed $\pi$-manifolds. We show that a closed, $k$-connected, $\pi$-manifold of dimension (2n + 1) that bounds a $\pi$-manifold, contact embeds in the $(4n-2k+3)$-dimensional…

In this note, we discuss embeddings of $3$--manifolds via open books. First we show that every open book of every closed orientable $3$--manifold admits an open book embedding in any open book decompistion of $S^2 \times S^3$ and $S^2…

Let $W$ be a nonorientable $4$-dimensional handlebody without $3$- and $4$-handles. We show that $W$ admits a Lefschetz fibration over the $2$-disk, whose regular fiber is a nonorientable surface with nonempty boundary. This is an analogue…

Spinal open book decompositions provide a natural generalization of open book decompositions. We show that any minimal symplectic filling of a contact 3-manifold supported by a planar spinal open book is deformation equivalent to the…

In this second paper of a two-part series, we prove that whenever a contact 3-manifold admits a uniform spinal open book decomposition with planar pages, its (weak, strong and/or exact) symplectic and Stein fillings can be classified up to…

Here we prove that up to diffeomorphism every compact Stein manifold W of dimension 2n+2>4 admits a Lefschetz fibration over the two-disk with Stein regular fibers, such that the monodromy of the fibration is a symplectomorphism induced by…

We study Legendrian embeddings of a compact Legendrian submanifold $L$ sitting in a closed contact manifold $(M,\xi)$ whose contact structure is supported by a (contact) open book $\mathcal{OB}$ on $M$. We prove that if $\mathcal{OB}$ has…

Given two open books with equal pages we show the existence of an exact symplectic cobordism whose negative end equals the disjoint union of the contact manifolds associated to the given open books, and whose positive end induces the…

The purpose of this article is to study co-dimension $2$ iso-contact embeddings of closed contact manifolds. We first show that a closed contact manifold $(M^{2n-1}, \xi_M)$ iso-contact embeds in a contact manifold $(N^{2n+1}, \xi_N),$…

In this note we observe that one can contact embed all contact 3-manifolds into a Stein fillable contact structure on the twisted $S^3$-bundle over $S^2$ and also into a unique overtwisted contact structure on $S^3\times S^2$. These results…

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…

We give an elementary topological obstruction for a manifold $M$ of dimension $2q{+}1 \geq 7$ to admit a contact open book with flexible Weinstein pages and $c_1(\pi_2(M)) = 0$: if the torsion subgroup of the $q$-th integral homology group…

The first goal of this paper is to construct examples of higher dimensional contact manifolds with specific properties. Our main results in this direction are the existence of tight virtually overtwisted closed contact manifolds in all…

We construct open book structures on all moment-angle manifolds and describe the topology of their leaves and bindings under certain restrictions. II. We also show, using a recent deep result about contact forms due to Borman, Eliashberg…

A real 3- or 4-manifold has by definition an orientation preserving smooth involution acting on it. We consider Lefschetz fibrations of 4-dimensional manifolds-with-boundary and open book decompositions on their boundary in the existence of…

We show the existence of a contractible periodic Reeb orbit for any contact structure supported by an open book whose binding can be realised as a hypersurface of restricted contact type in a subcritical Stein manifold. A key ingredient in…