Related papers: The embedding problem in topological dynamics and …

First, we prove a special case of Knaster's problem, implying that each symmetric convex body in R^3 admits an inscribed cube. We deduce it from a theorem in equivariant topology, which says that there is no S_4-equivariant map from SO(3)…

We discuss and prove a theorem which asserts that any n-dimensional semi-Riemannian manifold can be locally embedded in a (n+1)-dimensional space with a non-degenerate Ricci tensor which is equal, up to a local analytic diffeomorphism, to…

Let $X/K$ be a variety over a field, and $A/K$ an abelian variety. A regular homomorphism to $A$ (in codimension $i$) induces, for every smooth geometrically connected pointed $K$-scheme $(T,t_0)$ and every cycle class $Z \in CH^i(T\times…

A topological classification of many classes of dynamical systems with regular dynamics in low dimensions is often reduced to combinatorial invariants. In dimension 3 combinatorial invariants are proved to be insufficient even for simplest…

It is shown that if a $T_2$ topological space $X$ contains a closed uncountable discrete subspace, then the spaces $(\omega_1 + 1)^{\omega}$ and $(\omega_1 + 1)^{\omega_1}$ embed into $(CL(X),\tau_F)$, the hyperspace of nonempty closed…

When a discrete group admits a convex-cocompact action on a non-compact rank-one symmetric space, there is a natural lower bound for the Hausdorff dimension of the limit set, given by the Ahlfors regular conformal dimension of the boundary…

A classical result by Poznyak asserts that any smooth $2$-dimensional Riemannian metric $g$, posed on the closure of a simply connected domain $\omega\subset\mathbb{R}^2$, has a smooth isometric immersion into $\mathbb{R}^4$. Using…

Let $K$ be an $(n-1)$-dimensional piecewise linear sphere on $[m]$, where $m\leq n+4$. There are a canonical action of $m$-dimensional torus $T^m$ on the moment-angle complex $\mathcal{Z}_K$, and a canonical action of $\mathbb{Z}_2^m$ on…

We investigate when a linear functional $L$ defined on a linear subspace $B$ of a unital commutative real algebra $A$ admits an integral representation w.r.t. a positive Radon measure supported on a closed subset $K$ of the character space…

We consider a theory in which spacetime is an n-dimensional surface $V_n$ embedded in an $N$-dimensional space $V_N$. In order to enable also the Kaluza-Klein approach we admit $n > 4$. The dynamics is given by the minimal surface action in…

We establish a general spectral gap theorem for actions of products of groups which may replace Kazhdan's property (T) in various situations. As a main application, we prove that a confined subgroup of an irreducible lattice in a higher…

It is shown that for every $K>0$ and $\e\in (0,1/2)$ there exist $N=N(K)\in \N$ and $D=D(K,\e)\in (1,\infty)$ with the following properties. For every separable metric space $(X,d)$ with doubling constant at most $K$, the metric space…

Trickle-down is a phenomenon in high-dimensional expanders with many important applications -- for example, it is a key ingredient in various constructions of high-dimensional expanders or the proof of rapid mixing for the basis exchange…

We prove a universal embedding theorem for flag manifolds: every flag manifold admits a holomorphic isometric embedding into an irreducible classical flag manifold. This result generalizes the classical celebrated embedding theorems of…

Thanks to Pfaffian techniques, we study the R\'enyi entanglement entropies and the entanglement spectrum of large subsystems for two-dimensional Rokhsar-Kivelson wave functions constructed from a dimer model on the triangular lattice. By…

Starting with topological field theories we investigate the Ray-Singer analytic torsion in three dimensions. For the lens Spaces L(p;q) an explicit analytic continuation of the appropriate zeta functions is contructed and implemented. Among…

Working over a field $k$ of characteristic zero, we study the ring $\mathfrak{R}=\mathfrak{D}^{\mathbb{Z}_2}$ where $\mathfrak{D}=k[x_0,x_1,x_2]/(2x_0x_2-x_1^2-1)$ and $\mathbb{Z}_2$ acts by $x_i\to -x_i$. $\mathfrak{D}$ admits an algebraic…

Recently it was shown that the topological entanglement entropy (TEE) of a two-dimensional gapped ground state obeys the universal inequality $\gamma \geq \log \mathcal{D}$, where $\gamma$ is the TEE and $\mathcal{D}$ is the total quantum…

Let $K\in L^1(\mathbb R)$ and let $f\in L^\infty(\mathbb R)$ be two functions on $\mathbb R$. The convolution $$(K\ast f)(x)=\int_{\mathbb R}K(x-y)f(y)dy$$ can be considered as an average of $f$ with weight defined by $K$. Wiener's…

In this article we describe the $G_{comp}\times G_{comp}$-equivariant topological $K$-ring of a {\em cellular} toroidal embedding $\mathbb{X}$ of a complex connected reductive algebraic group $G$. In particular, our results extend the…