Related papers: Nonexistence of k-bounded sobrification

Let $X$ be a discrete metric space with bounded geometry. We show that if $X$ admits an "A-by-CE coarse fibration", then the canonical quotient map $\lambda: C^*_{\max}(X)\to C^*(X)$ from the maximal Roe algebra to the Roe algebra of $X$,…

We construct two dcpo's whose Scott spaces are sober, but the Scott space of their order product is not sober. This answers an open problem on the sobriety of Scott spaces. Meantime, we show that if $M$ and $N$ are special type of sober…

We give a complete classification of umbilical surfaces of arbitrary codimension of a product $Q^{n_1}_{k_1}\times Q^{n_2}_{k_2}$ of space forms whose curvatures satisfy $k_1 + k_2 \not= 0$.

We construct a simple, separable, unital, and nuclear C*-algebra with weakly unperforated K_0-group which does not absorb the Jiang-Su algebra Z tensorially. As a result, we obtain a stably finite counter-example to Elliott's classification…

We compute rationally the topological (complex) K-theory of the classifying space BG of a discrete group provided that G has a cocompact G-CW-model for its classifying space for proper G-actions. For instance word-hyperbolic groups and…

Let $T^n$ be the real $n$-torus group. We give a new definition of lens spaces and study the diffeomorphic classification of lens spaces. We show that any $3$-dimensional lens space $L(p; q)$ is $T^2$-equivariantly cobordant to zero. We…

We investigate what we call generalized ovoids, that is families of totally isotropic subspaces of finite classical polar spaces such that each maximal totally isotropic subspace contains precisely one member of that family. This is a…

We show that the category $L\textbf{-Top}_{0}$ of $T_{0}$-$L$-topological spaces is the epireflective hull of Sierpinski $L$-topological space in the category $L\textbf{-Top}$ of $L$-topological spaces and the category $L\textbf{-Sob}$ of…

We prove that some well known compact quantum spaces like quantum tori and some quantum two-spheres do not admit a compact quantum group structure. This is achieved by considering existence of traces, characters and nuclearity of the…

We give new characterizations of spaces $X$ which are $k_\mathbb{R}$-spaces or $s_\mathbb{R}$-spaces. Applying the obtained results we provide some sufficient and necessary conditions on $X$ for which $C_p(X)$ is a $k_\mathbb{R}$-space or…

We introduce the notion of a totally ($K$-) bounded element of a W*-probability space $(M, \varphi)$ and, borrowing ideas of Kadison, give an intrinsic characterization of the $^*$-subalgebra $M_{tb}$ of totally bounded elements. Namely, we…

Our contribution is a bounded cubic compilation theorem. For each fixed resource parameter $k$, syntactic proof checking at resource level $k$ is faithfully represented by a finite bounded-domain system of cubic polynomial equations. Every…

We prove that zero sets for distinct Fock spaces are not the same, this is an answer of a question asked by K. Zhu in \cite[Page. 209]{Zhu}.

Irreducible representations of quantum groups $SL_q(2)$ (in Woronowicz' approach) were classified in J.Wang, B.Parshall, Memoirs AMS 439 in the~case of $q$ being an~odd root of unity. Here we find the~irreducible representations for all…

We propose a notion of cusp forms on semisimple symmetric spaces. We then study the real hyperbolic spaces in detail, and show that there exists both cuspidal and non-cuspidal discrete series. In particular, we show that all the spherical…

When R is a commutative ring with identity, and if k is a natural number with kR = R, then C. Weibel proved that SK_1(R[X]) has no k-torsion. We reprove his result for any associative ring R with identity in which kR = R.

Let $ G $ be a real simple linear connected Lie group of real rank one. Then, $ X := G/K $ is a Riemannian symmetric space with strictly negative sectional curvature. By the classification of these spaces, $X$ is a real/complex/quaternionic…

Let $X$ be a non-positively curved cube complex with hyperbolic fundamental group. We prove that $\pi_1(X)$ has a non-free subgroup of infinite index unless $\pi_1(X)$ is either free or a surface group, answering questions of Gromov and…

We provide sharp forms of $k$-plane transform inequalities on the $d$-dimensional sphere $\mathbb{S}^d$ and the $d$-dimensional hyperbolic space $\mathbb{H}^d$. In particular, we prove that extremizers do not exist for $\mathbb{H}^d$. This…

We show that the Baum-Connes morphism twisted by a non-unitary representation, defined in [GA08], is an isomorphism for a large class of groups satisfying the Baum-Connes conjecture. Such class contains all the real semi-simple Lie groups,…