The aim of this paper is to give an alternative proof of a theorem about the existence of contact structures on five-manifolds due to Geiges. This theorem asserts that simply-connected five-manifolds admit a contact structure in every homotopy class of almost contact structures. Our proof uses the open book constructio…
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23 results for “five-manifolds”
Defines and proves CR invariants on five-manifolds.
problem Defines and studies CR invariants on CR five-manifolds.
method Defines global secondary CR invariants and proves their linear combination.
result Any global secondary CR invariant is a linear combination of total -curvature, total -curvature, and a local CR invariant.
We construct rigid supersymmetric gauge theories on Riemannian five-manifolds. We follow a holographic approach, realizing the manifold as the conformal boundary of a six-dimensional bulk supergravity solution. This leads to a systematic classification of five-dimensional supersymmetric backgrounds with gravity duals. …
New operators for -curvature on 5D pseudohermitian manifolds.
problem Characterizing CR manifolds with -flat contact forms.
method Constructing -curvature operators on specific forms.
result New formula for scalar -curvature and cohomological characterization of CR manifolds.
A new algebraic method extracts symmetry anomalies from 5D SCFTs.
problem Extracting global symmetry anomalies from 5D superconformal field theories.
method Path algebra of branes probing Calabi-Yau cones provides a complementary approach.
result Combinatorial approach to symmetry anomalies in 5D SCFTs.
The topological obstructions to the existence of an irreducible SO(3) structure on a five manifoldmath.DG
A nonstandard (maximal) inclusion SO(3) in SO(5) associated with the irreducible representation ρ_5 of SO(3) in R^5 is considered. The topological obstructions for admitting the SO(3) structure on the frame bundle over 5-manifold are investigated. The necessary and sufficient conditions are formulated.
Novel gauge-theoretic Floer homologies defined for 7, 6, and 5-manifolds.
problem Defining novel gauge-theoretic Floer homologies for different dimensions.
method Topologically-twisted 8d gauge theory on Spin(7)-manifolds.
result Derivation of novel Floer homologies and -categories.
We study null Sasakian structures in dimension five. First, based on a result due to Kollár [Ko], we improve a result by Boyer, Galicki and Matzeu in [BGM] and prove that simply connected manifolds diffeomorphic to $# k(S^2\times S^3)$ admit null Sasaki -Einstein structures if and only if . After…
For each invariant polynomial , we construct a global CR invariant via the renormalized characteristic form of the Cheng--Yau metric on a strictly pseudoconvex domain. When the degree of is 0, the invariant agrees with the total -curvature. When the degree is equal to the CR dimension, we construct a primed …
Given a simply connected, closed four manifold, we associate to it a simply connected, closed, spin five manifold. This leads to several consequences : the stable and unstable homotopy groups of such a four manifold is determined by its second Betti number, and the ranks of the homotopy groups can be explicitly calcula…
We construct branched double coverings by certain direct products of manifolds for connected sums of copies of sphere bundles over the 2-sphere. As an application we answer a question of Kotschick and Loeh up to dimension five. More precisely, we show that: (1) every simply connected, closed four-manifold admits a bran…
The paper proves finite Urysohn 1-width for 4 and 5 manifolds with positive biRicci curvature.
problem Proving finite Urysohn 1-width for 4 and 5 manifolds with positive biRicci curvature.
method Using positive biRicci curvature and uniform scalar curvature bounds, the paper shows that the Urysohn 1-width is finite and depends only on the curvature bounds.
result Closed 4 and 5 manifolds with positive biRicci curvature have finite Urysohn 1-width, which depends only on the curvature bounds.
Two constructions of contact manifolds are presented: (i) products of S^1 with manifolds admitting a suitable decomposition into two exact symplectic pieces and (ii) fibre connected sums along isotropic circles. Baykur has found a decomposition as required for (i) for all closed, oriented 4-manifolds. As a corollary, w…
Negative Sasakian manifolds, where the first Chern class of the contact subbundle is a torsion class, can be viewed as Seifert- bundles where the base orbifold has an ample orbifold canonical class. We use this framework to settle completely an open problem formulated by C.Boyer and K.Galicki which asks whether or…
Associated to the problem of rolling one surface along another there is a five-manifold M with a rank two distribution. If the two surfaces are spheres then M is the product of the rotation group SO_3 with the two-sphere and its distribution enjoys an obvious symmetry group; the product of two SO_3's, one for each sphe…
Defines Killing spinors and bosonic backgrounds in 5D supergravity.
problem Characterizing backgrounds in 5D supergravity.
method Calculates Spencer cohomology, defines Killing spinors, and imposes constraints on spinor connection curvature.
result Recover field equations of 5D supergravity and find new field equations for -valued one-form.
On simply connected five manifolds Sasakian-Einstein metrics coincide with Riemannian metrics admitting real Killing spinors which are of great interest as models of near horizon geometry for three-brane solutions in superstring theory [KW]. We expand on the recent work of Demailly and Kollár [DK] and Johnson and Kollá…
There are two well-known parabolic split -geometries in dimension five, -distributions and -contact structures. Here we link these two geometries with yet another -related contact structure, which lives on a seven-manifold. We present a natural geometric construction of a Lie contact structure o…
New operators and curvatures derived from embedded manifolds.
problem Finding obstructions and coupling extrinsic operators.
method Explicit computation of extrinsic Paneitz operator and its applications.
result New extrinsically-coupled fourth and sixth order operators.
Topological Gauge Theories with Sixteen Supercharges: Higher -categorification of Floer Homologieshep-th
Novel -categories derived from gauge theories for manifold homologies.
problem Categorifying manifold homologies via gauge theories.
method 3d and 8d gauged Landau-Ginzburg models, higher -categories.
result Derived novel -categories for various manifold homologies.
In the literature, there are two different versions of Hard Lefschetz theorems for a compact Sasakian manifold. The first version, due to Kacimi-Alaoui, asserts that the basic cohomology of a compact Sasakian manifold satisfies the transverse Lefschetz property. The second version, established far more recently by Capp…
5D gauge theories are dual to 3D and 2D models via Floer homologies.
problem Exploring dualities in 5D gauge theories and their 3D and 2D counterparts.
method Using Landau-Ginzburg models and Floer homologies, the paper establishes dualities between different gauge theories and their associated homologies.
result Dual -categories of Floer homologies are derived, proving mirror symmetry and Langlands duality.
Constructs perturbed Fefferman spaces on almost CR manifolds.
problem Characterize and construct conformal structures on almost CR manifolds.
method Introduces perturbations of Fefferman spaces using semi-basic one-forms.
result Derives conditions for conformally flat spaces on zero sets of almost Einstein scales.