arXiv research

Survey on CR Paneitz operator and manifold embeddability.

Characterizes Lorentzian manifolds embeddable in Minkowski spacetime.

The paper improves embedding results for $CR$ submanifolds, showing that compact deformations stay embeddable.

Research shows that certain metric spaces cannot contain rigid structures and provides evidence for loose embeddings into Euclidean spaces.

We show that every analytic semi-Riemannian manifold can be isometrically embeddded into an Einstein maifold in co-dimension one.

It is shown that the space of null geodesics of a causally simple Lorentzian manifold is Hausdorff if it admits an open conformal embedding into a globally hyperbolic spacetime. This provides an obstruction to conformal embeddings of causally simple spacetimes into globally hyperbolic ones irrespective of curvature con…

The paper characterizes graph manifolds using fold maps and embeddability of polyhedra.

Embeddability of simplicial complex $[3]*K$ linked to $K$'s embeddability.

The paper explores embedding Ricci flow solutions in flag manifolds.

Criterion for manifold skeletons embeddability in Euclidean space.

We characterize those spacetimes which admit a isometric (or conformal) embedding in some Lorentz-Minkowski space L^N. In particular, any globally hyperbolic spacetime can be isometrically embedded in L^N. This is proven by a result of its own interest: the construction of a smooth time function whose gradient is bound…

Criteria found for graph drawings on surfaces.

Paper proves nonnegativity of CR Paneitz operator for embeddable CR manifolds.

Study on CR Paneitz operator on non-embeddable CR manifolds.

We give series of explicit examples of Levi-nondegenerate real-analytic hypersurfaces in complex spaces that are not transversally holomorphically embeddable into hyperquadrics of any dimension. For this, we construct invariants attached to a given hypersurface that serve as obstructions to embeddability. We further st…

CR Paneitz operator on non-embeddable tori has infinitely many negative eigenvalues

This paper studies CR manifolds and embeddability in complex spaces.

Defines coupled embeddability for maps on products of spaces, generating examples and nonexamples.

Let $Γ$ be a finitely generated group which is hyperbolic relative to a finite family $\{H_1,...,H_n\}$ of subgroups. We prove that $Γ$ is uniformly embeddable in a Hilbert space if and only if each subgroup $H_i$ is uniformly embeddable in a Hilbert space.

Study convex embeddability in linear and circular orders, applying to knots.

A pseudocircle is a simple closed curve on some surface; an arrangement of pseudocircles is a collection of pseudocircles that pairwise intersect in exactly two points, at which they cross. Ortner proved that an arrangement of pseudocircles is embeddable into the sphere if and only if all of its subarrangements of size…

Study embeddability of 2-complexes in 4-space, proving Heawood family's excluded minors.

We show that a space with a finite asymptotic dimension is embeddable in a non-positively curved manifold. Then we prove that if a uniformly contractible manifold X is uniformly embeddable in $\R^n$ or non-positively curved n-dimensional simply connected manifold then $X\times\R^n$ is integrally hyperspherical. If a un…

An arrangement of pseudocircles is a finite set of oriented closed Jordan curves each two of which cross each other in exactly two points. To describe the combinatorial structure of arrangements on closed orientable surfaces, in (Linhart, Ortner 2004) so-called *intersection schemes* were introduced. Building up on res…

New bounds on maximal linkless graphs with improved edge-to-vertex ratios.

The paper studies branched surfaces and their properties.

Study finds maximal linklessly embeddable graphs up to 11 vertices and their complements.

Klein bottle embeds into specific lens spaces.

New findings on embedding simplicial complexes, showing instability under joins.

Study explores associated groups of symmetric quandles and their properties.

New graphs found that can be drawn without crossing links.

Graphs embeddable on torus and linklessly in 3D can be embedded linklessly in standard torus.

New proof shows non-embeddable polyhedra and conditions for embedding products.

Polynomial-time algorithm for c-planarity and thickenability.

CR Q-curvature flow solves CR manifold curvature conjecture.

Groups can act on 3-manifolds if their Cayley complex can embed in specific types of 3-manifolds.

Graphs and their complements are intrinsically knotted.

Proofs show embedding conditions for complex joins and factors.

We study the fillability (or embeddability) of 3-dimensional $CR$ structures under the geometric flows. Suppose we can solve a certain second order equation for the geometric quantity associated to the flow. Then we prove that if the initial $CR$ structure is fillable, then it keeps having the same property as long as …

The study characterizes embeddable 2-complexes in 3-space.

In this paper, we study lower bounds on the K-theory of the maximal $C^*$-algebra of a discrete group based on the amount of torsion it contains. We call this the finite part of the operator K-theory and give a lower bound that is valid for a large class of groups, called the "finitely embeddable groups". The class of …

Quantum isometry groups extend to all countable metric spaces, and loose embeddings help understand metric space relationships.

New graph shows edge deletion/contraction doesn't always result in intrinsically linked graphs.

Characterizes embeddable relations in Euclidean space.

We analyze an algorithmic question about immersion theory: for which $m$, $n$, and $CAT=\mathbf{Diff}$ or $\mathbf{PL}$ is the question of whether an $m$-dimensional $CAT$-manifold is immersible in $\mathbb{R}^n$ decidable? As a corollary, we show that the smooth embeddability of an $m$-manifold with boundary in $\math…

It is proved that the suspension of a closed n-dimensional manifold M, $n\ge1$, does not embed in a product of n+1 curves. In fact, the ultimate result will be proved in a much more general setting. This is a far-reaching generalization the Borsuk theorem on non-embeddability of the (n+1)-dimensional sphere in a produc…

CR 3-sphere rigidity proven through curvature invariant.

S. Parsa proved embedding conditions for simplicial joins.