Related papers: On universal parity on free two-dimensional knots

We prove the Freiheitssatz for the variety of generic Poisson algebras.

Given a group endowed with a Z/2-valued morphism we associate a Gauss diagram theory, and show that for a particular choice of the group these diagrams encode faithfully virtual knots on a given arbitrary surface. This theory contains all…

We prove the existence of a global attractor for the Newton-Boussinesq equation defined in a two-dimensional channel. The asymptotic compactness of the equation is derived by the uniform estimates on the tails of solutions. We also…

We prove that a random distribution in two dimensions which is conformally invariant and satisfies a natural domain Markov property is a multiple of the Gaussian free field. This result holds subject only to a fourth moment assumption.

We prove a general multidimensional invariance principle for a family of U-statistics based on freely independent non-commutative random variables of the type $U_n(S)$, where $U_n(x)$ is the $n$-th Chebyshev polynomial and $S$ is a standard…

A positive definite Hermitian lattice is said to be 2-universal if it represents all positive definite binary Hermitian lattices. We find all 2-universal ternary and quaternary Hermitian lattices over imaginary quadratic number fields.

We introduce a special class of knots, called global knots, in F^2 x R and we construct new isotopy invariants, called T-invariants, for global knots. Some T-invariants are of finite type but they cannot be extracted from the generalized…

In this paper, we prove some rigidity theorems for the entire 2-convex solutions of 2-Hessian equation in Euclidean space. As an application, we obtain a Bernstein type theorem for global special Lagrangian graphs.

In this paper, we establish a universal equality governing Euclidean integrals of gravitational actions in higher-derivative theories. This relation is shown to hold universally for asymptotically flat black holes in pure gravity, and is…

Gaussian universality results assert that the properties of many estimators remain unchanged when the input data are replaced by Gaussians. Such results have gained popularity in high-dimensional statistics and machine learning, as…

The present paper produces examples of Gauss diagram formulae for virtual knot invariants which have no analogue in the classical knot case. These combinatorial formulae contain additional information about how a subdiagram is embedded in a…

We show that the spectral dimension d_s of two-dimensional quantum gravity coupled to Gaussian fields is two for all values of the central charge c <= 1. The same arguments provide a simple proof of the known result d_s= 4/3 for branched…

Let N > n, and denote by K the convex hull of N independent standard gaussian random vectors in an n-dimensional Euclidean space. We prove that with high probability, the isotropic constant of K is bounded by a universal constant. Thus we…

We give a new proof of the straightening/unstraightening correspondence by proving a generalization of the univalence property of the universal coCartesian fibration.

It is proved that all finitely generated subgroups of generalized free product of two groups are finitely separable provided that free factors have this property and amalgamated subgroups are normal in corresponding factors and satisfy the…

We show how to formulate a lattice gauge theory whose naive continuum limit corresponds to two-dimensional (Euclidean) quantum gravity including a positive cosmological constant. More precisely the resultant continuum theory corresponds to…

We prove that for some knot-like objects one can easily recognize non-equivalence w.r.t. all Reidemeister moves by studying some equivalence classes modulo only 2nd Reidemeister moves. There are applications to virtual knots, graph-links…

Let A be a basic finite dimensional and connected algebra over an algebraically closed field k with zero characteristic. If the ordinary quiver of A has no double bypasses, we show that A admits a Galois covering which satisfies a universal…

Let F be a perfect field. Then the diagonal quadratic form $a_iX_i^2$ over $F$ is universal over $M_2(F)$ if and only if atleast two of the $a_i$ are non-zero.

In this Letter we consider a general quadratic parity-preserving theory for a general flat connection. Imposing a local symmetry under the general linear group singles out the general teleparallel equivalent of General Relativity carrying…