arXiv research

Survey on CR Paneitz operator and manifold embeddability.

Criterion for manifold skeletons embeddability in Euclidean space.

Criteria found for graph drawings on surfaces.

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.

We relate the embeddability of the simplicial complex $[3]*K$ into $\mathbb{R}^{n+2}$ to that of $K$ into $\mathbb{R}^n$. In brief, the embeddability of $K$ into $\mathbb{R}^n$, in the metastable range $2n\geq 3(d+1)$, is equivalent to the embeddability of $[3]*K$ into $\mathbb{R}^{n+2}$. We show moreover than the van …

Characterizes Lorentzian manifolds embeddable in Minkowski spacetime.

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.

The nonnegativity of the CR Paneitz operator plays a crucial role in three-dimensional CR geometry. In this paper, we prove this nonnegativity for embeddable CR manifolds. This result and previous works give an affirmative solution of the CR Yamabe problem for embeddable CR manifolds. We also show the existence of a co…

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…

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…

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

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.

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

Klein bottle embeds into specific lens spaces.

We study the atomic embeddability testing problem, which is a common generalization of clustered planarity (c-planarity, for short) and thickenability testing, and present a polynomial-time algorithm for this problem, thereby giving the first polynomial-time algorithm for c-planarity. C-planarity was introduced in 1995…

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

New graphs found that can be drawn without crossing links.

Study explores associated groups of symmetric quandles and their properties.

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.

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

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

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.

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

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 …

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

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…

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

CR 3-sphere rigidity proven through curvature invariant.

The problem of identifying geometric structure in heterogeneous, high-dimensional data is a cornerstone of representation learning. While there exists a large body of literature on the embeddability of canonical graphs, such as lattices or trees, the heterogeneity of the relational data typically encountered in practic…

S. Parsa proved embedding conditions for simplicial joins.

The study proves CR structures on specific three-manifolds are equivalent to standard structures.

The intrinsic geometry of the Kerr ergosurface on constant Boyer-Lindquist (BL), Kerr, and Doran time slices is characterized. Unlike the BL slice, which had been previously studied, the other slices (i) do not have conical singularities at the poles (except the Doran slice in the extremal limit), (ii) have finite pola…

We show that an n-dimensional compactum X embeds in R^m, where m>3(n+1)/2, if and only if X x X - Δadmits an equivariant map to S^{m-1}. In particular, X embeds in R^{2n}, n>3, iff the top power of the (twisted) Euler class of the factor-exchanging involution on X x X - Δis trivial. Assuming that X quasi-embeds in R^{2…

Paper characterizes embeddability of function spaces into $L_p$-type RKBS via metric entropy.

Criteria for embedding simplicial complexes into manifolds, reducing a topological problem to algebra.

In this paper we prove new embedding results for compactly supported deformations of $CR$ submanifolds of $\mathbb{C}^{n+d}$: We show that if $M$ is a $2$-pseudoconcave $CR$ submanifold of type $(n,d)$ in $\mathbb{C}^{n+d}$, then any compactly supported $CR$ deformation stays in the space of globally $CR$ embeddable in…

The paper calculates variations of Einstein-Hilbert action on CR manifolds.