arXiv research

Common positive stabilisation found for isotopic contact structures.

A Sasakian structure on a manifold is called {\it positive} if its basic first Chern class can be represented by a positive (1,1)-form with respect to its transverse holomorphic CR-structure. We prove a theorem that says that every positive Sasakian structure can be deformed to a Sasakian structure whose metric has pos…

The aim of this paper is to study compact 5--manifolds which carry a positive Sasakian structure. Strong restrictions are derived for the integral homology groups. In some cases, all positive Sasakian structures are classified. A key step is to study log Del Pezzo surfaces whose boundary divisor contains positive genus…

Establishes geometric properties of elements in the positive semigroup of a general real semisimple Lie group.

We develop the structure theory of full isometry groups of locally compact non-positively curved metric spaces. Amongst the discussed themes are de Rham decompositions, normal subgroup structure and characterising properties of symmetric spaces and Bruhat--Tits buildings. Applications to discrete groups and further dev…

Positivity of intersections in 4-manifolds leads to taming symplectic structures.

Proves positive mass theorem on conical manifolds with small angles.

Solves open problems on curved projective varieties.

Positive injectivity radius for manifolds with Lie structure at infinity.

This paper studies symplectic structures on elliptic surfaces with positive Euler number.

A flow from hypersymplectic to hyperkähler structures is described.

It is well known that if the dimension of the Sasaki cone is greater than one, then all Sasakian structures are either positive or indefinite. We discuss the phenomenon of type changing within a fixed Sasaki cone. Assuming henceforth that the dimension of the Sasaki cone is greater than one, there are three possibiliti…

New open books defy positive factorisation in genus one.

The paper develops a theory of Ehresmann structures in positive characteristic.

The paper extends structure theorem to projective klt varieties with specific tangent sheaf properties.

Positive surgery on knots in weakly fillable 3-manifolds yields weakly fillable contact structures.

Study on sets with positive reach in Euclidean and Riemannian spaces.

In this paper, we consider a closed 3-manifold $M$ with flat conformal structure $C$. We will prove that, if the Yamabe constant of $(M, C)$ is positive, then $(M, C)$ is Kleinian.

No conformal product structures on compact manifolds with constant curvature.

Introduces $Θ$-positivity in Lie groups, generalizing Lusztig's positivity.

This paper provides an initial investigation on the application of convolutional neural networks (CNNs) for fingerprint-based positioning using measured massive MIMO channels. When represented in appropriate domains, massive MIMO channels have a sparse structure which can be efficiently learned by CNNs for positioning …

The paper explores curvature positivity on Kähler and quasi-Kähler flag manifolds.

New proof shows 4-manifolds can't support complex structures.

This paper formalizes manifolds in positive characteristic varieties.

We show that the twisted SL(2) skein algebra of a surface has a natural basis (the bracelets basis) that is positive, in the sense that the structure constants for multiplication are positive integers.

It is shown how the well-known class of bihamiltonian structures in general position can be extended to a wider class. A generalization of the corresponding notion of a Veronese web for this wider class is presented (in the general position case Veronese webs form complete systems of local invariants for bihamiltonian …

Characterizes real left symmetric algebras with positive definite Koszul form and related Kähler-Einstein structures.

This paper proves a map from flow-spines to contact structures is surjective.

We investigate the possibility of desingularizing a positively curved metric cone by an expanding gradient Ricci soliton with positive curvature operator. This amounts to study the deformation of such geometric structures. As a consequence, we prove that the moduli space of conical positively curved gradient Ricci expa…

New insights into Markov chain geometry via positive transition measures.

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, connected, oriented 3-manifold is supported by a flow-spine if it has a contact form w…

Study of conformal limits for special opers in Lie groups.

The paper proves a discrete positive mass theorem for graphs.

Let Y(r) be the closed, oriented three-manifold obtained by performing rational r-surgery on the right-handed trefoil knot in the three-sphere. Using contact surgery and the Heegaard Floer contact invariants we construct positive, tight contact structures on Y(r) for every r not equal to 1. This implies, in particular,…

We introduce the notion of a positive opetope and positive opetopic cardinals as certain finite combinatorial structures. The positive opetopic cardinals to positive-to-one polygraphs are like simple graphs to free omega-categories over omega-graphs, c.f. [MZ]. In particular, they allow us to give an explicit combinato…

We introduce $Θ$-positivity, a new notion of positivity in real semisimple Lie groups. The notion of $Θ$-positivity generalizes at the same time Lusztig's total positivity in split real Lie groups as well as well known concepts of positivity in Lie groups of Hermitian type. We show that there are two other families of …

We discuss the Sasakian geometry of odd dimensional homotopy spheres. In particular, we give a completely new proof of the existence of metrics of positive Ricci curvature on exotic spheres that can be realized as the boundary of a parallelizable manifold. Furthermore, it is shown that on such homotopy spheres $\script…

Extended RDS filtering for positions and orientations, improving crossing structure enhancement and inpainting.

New open books solve a long-standing surface mapping class group question.

The space of metrics with positive Ricci curvature on spheres has special algebraic structures.

The paper predicts responses on out-of-sample nodes using latent positions on unknown curves.

Workshop notes on positivity in Lie groups and its applications.

Study connects contact structures to cone geodesics and contactomorphisms.

We derive the Riemannian Positive Mass theorem in arbitrary dimensions, without any topological constraints. The main new tools are skin structures and surgeries on minimal hypersurfaces.

Agol recently introduced the notion of a veering triangulation, and showed that such triangulations naturally arise as layered triangulations of fibered hyperbolic 3-manifolds. We prove, by a constructive argument, that every veering triangulation admits positive angle structures, recovering a result of Hodgson, Rubins…

Suppose $M_{1}$ and $M_{2}$ are $3$-dimensional closed (compact without boundary) CR manifolds with positive CR Yamabe constant. In this note, we show that the connected sum of $M_{1}$ and $M_{2}$ also admits a CR structure with positive CR Yamabe constant.

Noncommutative Kähler structures were recently introduced by the second author as a framework for studying noncommutative Kähler geometry on quantum homogeneous spaces. It was subsequently observed that the notion of a positive vector bundle directly generalises to this setting, as does the Kodaira vanishing theorem. I…

The aim of this paper is to present a direct and simple proof of a result concerning the existence of metrics of positive Ricci curvature on the total space of fiber bundles with compact structure groups. In particular, it also generalizes and puts in a unified framework the results in Nash \cite{nash} and Poor \cite{p…