Related papers: Elliptic open books on torus bundles over the circ…

Suppose S is a compact surface with boundary, and let g be a diffeomorphism of S which fixes the boundary pointwise. We denote by (M_{S,g},\xi_{S,g})$ the contact 3-manifold compatible with the open book (S,g). In this article, we construct…

We compute the Heegaard Floer homology of any rational homology 3-sphere with an open book decomposition of the form (T,\phi), where T is a genus one surface with one boundary component. In addition, we compute the Heegaard Floer homology…

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…

A flow-spine of a 3-manifold is a spine admitting a flow that is transverse to the spine, where the flow in the complement of the spine is diffeomorphic to a constant flow in an open ball. We say that a contact structure on a closed,…

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…

A topological space is called self-covering if it is a nontrivial cover of itself. We prove that, under mild assumptions, a closed self-covering manifold with an abelian fundamental group fibers over a torus in various senses. As a…

In this note, we describe a procedure to construct generalized complex structures with an arbitrarily large number of type change loci on products of the circle with a connected sum of closed 3-manifolds. The loci need not be isotopic.

An interesting question in symplectic topology, which was posed by C. H. Taubes, concerns the topology of closed (i.e. compact and without boundary) connected oriented three dimensional manifolds whose product with a circle admits a…

This is a collection of results on the topology of toric symplectic manifolds. Using an idea of Borisov, we show that a closed symplectic manifold supports at most a finite number of toric structures. Further, the product of two projective…

We construct an open book decomposition compatible with a contact structure given by a rational contact surgery on a Legendrian link in the standard contact $S^3$. As an application we show that some rational contact surgeries on certain…

In this paper we study the (equivariant) topological types of a class of 3-dimensional closed manifolds (i.e., 3-dimensional small covers), each of which admits a locally standard $(\mathbb{Z}_2)^3$-action such that its orbit space is a…

According to Lerman, compact connected toric contact 3-manifolds with a non-free toric action whose moment cone spans an angle greater than $\pi$ are overtwisted, thus non-fillable. In contrast, we show that all compact connected toric…

We prove that for any closed, connected, oriented 3-manifold M, there exists an infinite family of 2-fold branched covers of M that are hyperbolic 3-manifolds and surface bundles over the circle with arbitrarily large volume.

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…

In this paper we explore algebraic and geometric structures that arise on parallelizable manifolds. Given a parallelizable manifold $\mathbb{L}$, there exists a global trivialization of the tangent bundle, which defines a map…

We introduce the notion of a nested open book, a submanifold equipped with an open book structure compatible with an ambient open book, and describe in detail the special case of a push-off of the binding of an open book. This enables us to…

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…

We construct new examples of manifolds with cyclic-parallel Ricci tensor, so called A-manifolds, on a r-torus bundle over a product of almost Hodge A-manifolds.

Iterated planar contact manifolds are a generalization of three dimensional planar contact manifolds to higher dimensions. We study some basic topological properties of iterated planar contact manifolds and discuss several examples and…

We study smooth proper embeddings of compact orientable surfaces in compact orientable $4$-manifolds and elements in the mapping class group of that surface which are induced by diffeomorphisms of the ambient $4$-manifolds. We call such…