arXiv research

Survey on open manifolds with nonnegative Ricci curvature and open questions.

Study shows range of simplicial volumes for open manifolds.

The abstract discusses embedding manifolds in open books and contact structures.

First example of open manifold with positive Ricci curvature and non-proper Busemann function.

Survey of recent scalar curvature results on open 3-manifolds.

New 4D shapes can't be opened like books.

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 $S^2 \widetilde{\times} S^3$ with the page a disk bundle over $S^2$ and monodromy the iden…

Handles decompositions reveal new open book structures.

The paper introduces foliated open books for contact 3-manifolds with boundary foliations.

Study finds open manifolds without complete metrics with positive scalar curvature.

New examples show high twisting doesn't guarantee open book maximality.

Proves codimension 2 spun embedding for specific manifolds.

Flat open manifolds with full first Betti number have zero curvature.

An open book decomposition of a 3-manifold $M$ induces a Heegaard splitting for $M$, and the minimal genus among all Heegaard splittings induced by open book decompositions is called the \emph{open book genus} of $M$. It is conjectured by Ozbagci \cite{O} that the open book genus is additive under the connected sum of …

We give a complete classification of foliations on open contact manifolds whose leaves are contact submanifolds of the ambient manifold. The results are analogues of Haefliger's classification of foliations on open manifold.

A real 3-manifold is a smooth 3-manifold together with an orientation preserving smooth involution, called a real structure. In this article we study open book decompositions on smooth real 3-manifolds that are compatible with the real structure. We call them real open book decompositions. We show that each real open b…

New proof of Giroux Correspondence for tight contact 3-manifolds.

Study open 3-manifolds as sums of closed ones, finding a classification.

The authors introduce Morse foliated open books for studying contact manifolds.

Upper bound for conjugate radius in open manifolds with scalar curvature and spectrum constraints.

Explains hyperkähler manifolds and their properties.

We give a sufficient condition for an open 3-manifold to admit a decomposition along properly embedded open annuli and tori, generalizing the toric splitting of Jaco-Shalen and Johannson.

New tools classify symplectic fillings of contact 3-manifolds.

Algorithm trisects 4D book into three chapters.

The hyperbolization process affects the structure of manifolds.

Simplicial volume vanishes for 4-manifolds with open book decompositions.

Study links in contact manifolds using open books and overtwisted disks.

We describe explicit open books on arbitrary plumbings of oriented circle bundles over closed oriented surfaces. We show that, for a non-positive plumbing, the open book we construct is horizontal and the corresponding compatible contact structure is also horizontal and Stein fillable. In particular, we describe horizo…

We endow the group of invertible Fourier integral operators on an open}manifold with the structure of an ILH Lie group. This is done by establishing such structures for the groups of invertible pseudodifferential operators and contact transformations on an open manifold of bounded geometry, and gluing those together vi…

Dubrovin duality connects two F-manifolds on the universal curve.

Open manifolds can be covered by $\mathbb{R}^m$ with finite or infinite degree.

The paper compares spectral geometry in hyperbolic and spherical manifolds.

The compact-open topology is minimal on diffeomorphism and homeomorphism groups of most smooth manifolds.

We study algebraic conditions on a group G under which every properly discontinuous, isometric G-action on a Hadamard manifold has a G-invariant Busemann function. For such G we prove the following structure theorem: every open complete nonpositively curved Riemannian K(G,1) manifold that is homotopy equivalent to a fi…

In this note we present a characterization of those open n-manifolds (n>4), whose products with the real line are homeomorphic to interiors of compact (n+1)-manifolds with boundary.

We describe explicit horizontal open books on some Seifert fibered 3--manifolds. We show that the contact structures compatible with these horizontal open books are Stein fillable and horizontal as well. Moreover we draw surgery diagrams for some of these contact structures.

The study explores nonorientable 3-manifolds using open books and their monodromies.

We show that any open aspherical manifold of dimension n>3 is tangentially homotopy equivalent to an n-manifold whose universal cover is not homeomorphic to the Euclidean space.

We study a coverings of open books and virtually overtwisted contact manifolds using open book foliations. We show that open book coverings produces interesting examples such as transverse knots with depth grater than 1. We also demonstrate explicit examples of virtually overtwisted open books.

Proof that convex structures on manifolds are open and closed.

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 contact manifold associated to the open book with the same page and concatenated monod…

We show that if the monodromy of an open book decomposition has sufficiently high displacement distance, acting on the loop and arc complex for a page, then it is the unique minimal Euler characteristic open book for the manifold. In particular, we show that such an open book induces the unique (up to isotopy) minimal …

Open manifolds with nonnegative Ricci curvature and Euclidean volume growth have finitely generated fundamental groups.

This paper concerns the class of contractible open 3-manifolds which are ``locally finite strong end sums'' of eventually end-irreducible Whitehead manifolds. It is shown that whenever a 3-manifold in this class is a covering space of another 3-manifold the group of covering translations must be a free group. It follow…

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.

The paper proves properties of open manifolds with positive isotropic curvature.

The notion of an open collar is generalized to that of a pseudo-collar. Important properties and examples are discussed. The main result gives conditions which guarantee the existence of a pseudo-collar structure on the end of an open n-manifold (n > 6). This paper may be viewed as a generalization of Siebenmann's famo…

The first author in recent work with D. Gay developed the notion of a Morse structure on an open book as a tool for studying closed contact 3-manifolds. We extend the notion of Morse structure to extendable partial open books in order to study contact 3-manifolds with convex boundary.