arXiv research

Novel contact metric structures lead to supergravity solutions.

Study of differential spinors on three-manifolds with skew-torsion.

Locally homogeneous Lorentzian three-manifolds with recurrect curvature are special examples of Walker manifolds, that is, they admit a parallel null vector field. We obtain a full classification of the symmetries of these spaces, with particular regard to symmetries related to their curvature: Ricci and matter colline…

Study of special Lorentzian Lie groups with 4D isometry group, finding all are non-gradient expanding Ricci solitons.

k-Curvature homogeneous three-dimensional Walker metrics are described for k=0,1,2. This allows a complete description of locally homogeneous three-dimensional Walker metrics, showing that there exist exactly three isometry classes of such manifolds. As an application one obtains a complete description of all locally h…

Develops a duality for graphs in Riemannian and Lorentzian spaces with prescribed mean curvature.

Generalizes Fefferman's structure to CR three-manifolds with additional data.

Investigates parallel spinors on Lorentzian four-manifolds using differential geometry.

Adjacency defined for three-manifolds, linking them to the 3-sphere.

We prove two rigidity results for complete Riemannian three-manifolds of higher rank. Complete three-manifolds have higher spherical rank if an only if they are spherical space forms. Complete finite volume three-manifolds have higher hyperbolic rank if and only if they are hyperbolic space forms.

Motivated by classical theorems on minimal surface theory in compact hyperbolic three-manifolds, we investigate the questions of existence and deformations for least area minimal surfaces in complete noncompact hyperbolic three-manifold of finite volume. We prove any closed immersed incompressible surface can be deform…

New contact structures extend supergravity solutions.

We determine which three-manifolds are dominated by products. The result is that a closed, oriented, connected three-manifold is dominated by a product if and only if it is finitely covered either by a product or by a connected sum of copies of the product of the two-sphere and the circle. This characterization can als…

Study properties of group rings of three-manifold groups.

Proof that specific groups are quasi-isometrically rigid.

Quantum invariants of three-manifolds linked to mock theta functions.

This paper adresses the following problem: Given a closed orientable three-manifold M, are there at most finitely many closed orientable three-manifolds 1-dominated by M? We solve this question for the class of closed orientable graph manifolds. More presisely the main result of this paper asserts that any closed orien…

Three-manifolds with non-negative pinched Ricci curvature have complete Ricci flows.

We construct four-dimensional symplectic cobordisms between contact three-manifolds generalizing an example of Eliashberg. One key feature is that any handlebody decomposition of one of these cobordisms must involve three-handles. The other key feature is that these cobordisms contain chains of symplectically embedded …

Proves a quantum invariant conjecture for specific three-manifolds.

Proves rigidity for eigenvalue estimate on three-manifolds.

Determining the associated metrics we get a local classification of contact metric three manifolds.

Inspired by the role geometric structures play in our understanding of surfaces and three-manifolds, and Berger's observation that a surface of constant sectional curvature is determined up to local isometry by its Laplace spectrum, we explore the extent to which compact locally homogeneous three-manifolds are characte…

We define a Floer-homology invariant for knots in an oriented three-manifold, closely related to the holomorphic disk Floer homologies for three-manifolds defined in an earlier paper. We set up basic properties of these invariants, including an Euler characteristic calculation, behaviour under connected sums. Then, we …

We show how the space of complex spin structures of a closed oriented three-manifold embeds naturally into a space of quadratic functions associated to its linking pairing. Besides, we extend the Goussarov-Habiro theory of finite type invariants to the realm of compact oriented three-manifolds equipped with a complex s…

In this paper we prove a compactness theorem for constant mean curvature surfaces with area and genus bound in three manifold with positive Ricci curvature. As an application, we give a lower bound of first eigenvalue of constant mean curvature surfaces in three manifold with positive Ricci curvature.

We construct a hyperbolic three-manifold with trivial finite type invariants up to a given degree.

We study the space of smooth Riemannian structures on compact three-manifolds with boundary that satisfies a critical point equation associated with a boundary value problem, for simplicity, Miao-Tam critical metrics. We provide an estimate to the area of the boundary of Miao-Tam critical metrics on compact three-manif…

Study bounds CMC surface index in 3-manifolds using energy.

Using contact surgery we define families of contact structures on certain Seifert fibered three-manifolds. We prove that all these contact structures are tight using contact Ozsath-Szabo invariants. We use these examples to show that, given a natural number n, there exists a Seifert fibered three-manifold carrying at l…

In this article we study minimal flat Lorentzian surfaces in Lorentzian complex space forms. First we prove that, for minimal flat Lorentzian surfaces in a Lorentzian complex form, the equation of Ricci is a consequence of the equations of Gauss and Codazzi. Then we classify minimal flat Lorentzian surfaces in the Lore…

In this paper we classify symplectic Lefschetz fibrations (with empty base locus) on a four-manifold which is the product of a three-manifold with a circle. This result provides further evidence in support of the following conjecture regarding symplectic structures on such a four-manifold: if the product of a three-man…

We show that every continuous action of a finite group on a smooth three-manifold is a uniform limit of smooth actions.

It is well known that any three-manifold can be obtained by surgery on a framed link in $S^3$. Lickorish gave an elementary proof for the existence of the three-manifold invariants of Witten using a framed link description of the manifold and the formalisation of the bracket polynomial as the Temperley-Lieb Algebra. Ka…

It is shown that any closed three-manifold M obtained by integral surgery on a knot in the three-sphere can always be constructed from integral surgeries on a 3-component link L with each component being an unknot in the three-sphere. It is also interesting to notice that infinitely many different integral surgeries on…

We show the existence of tight contact structures on infinitely many hyperbolic three-manifolds obtained via Dehn surgeries along sections of hyperbolic surface bundles over circle.

Affine 3-manifolds with centralizing holonomy are complete.

In this paper we study an invariant for oriented three-manifolds with $b_1>0$, which is defined using Heegaard splittings and the theta divisor of a Riemann surface. The paper is divided into two parts, the first of which gives the definition of the invariant, and the second of which identifies it with more classical (…

I calculate optimistically asymptotic behaviors of the WRT SU(2) invariants for the three-manifolds obtained from the figure-eight knot by p-surgeries with p=0,1,2,...,10, from which one can extract volumes and the Chern-Simons invariants of these closed manifolds. I conjecture that this also holds for general closed t…

We give a simple proof of a result originally due to Dimca and Suciu: a group that is both Kaehler and the fundamental group of a closed three-manifold is finite. We also prove that a group that is both the fundamental group of a closed three-manifold and of a non-Kaehler compact complex surface is infinite cyclic or t…

This paper gives a summary of our approach to invariants of three manifolds via right integrals on finite dimensional Hopf algebras and their relation to the Kirby calculus.

Y. Benoist proved that if a closed three-manifold M admits an indecomposable convex real projective structure, then M is topologically the union along tori and Klein bottles of finitely many sub-manifolds each of which admits a complete finite volume hyperbolic structure on its interior. We describe some initial result…

We use topological quantum field theory to derive an invariant of a three-manifold with boundary. We then show how to use this invariant as an obstruction to embedding one three-manifold in another.

Defines metrics for Lorentzian spaces and explores maximal developments.

Study of a series of Lorentzian structures on SL(2,R) with SO(1,1) symmetry.

We prove that if the fundamental group of an arbitrary three-manifold -- not necessarily closed, nor orientable -- is a Kaehler group, then it is either finite or the fundamental group of a closed orientable surface.

The paper explores actions on metric spaces similar to 3D manifolds, proving rigidity results.

Study left-invariant Codazzi tensors and harmonic curvature on Lorentzian Lie groups.