Related papers: Analytic structure of $q$-pseudoconcave subsets of…

Let $N$ be a closed nonorientable surface with or without marked points. In this paper we prove that, for every finite full subgraph $\Gamma$ of $\mathcal{C}^{\mathrm{two}}(N)$, the right-angled Artin group on $\Gamma$ can be embedded in…

Let $G$ be a connected closed subgroup of $\mathrm{GL}_n(\mathbb{C})$ which is simple as a Lie group and which acts irreducibly on $\mathbb{C}^n$. Regarding both $G$ and its Lie algebra $\mathfrak{g}$ as subsets of $M_n(\mathbb{C})$, we…

Let $c\in (0, 1]$ be a real number and let $n$ be a sufficiently large integer. We prove that every $n$-vertex $c n$-regular graph $G$ contains a collection of $\lfloor 1/c \rfloor$ paths whose union covers all but at most $o(n)$ vertices…

In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency…

We show that the graph $$\Gamma_f=\{(z,f(z))\in{\Bbb C}^2: z\in S\}$$ in ${\Bbb C}^2$ of a function $f$ on the unit circle $S$ which is either continuous and quasianalytic in the sense of Bernstein or $C^\infty$ and quasianalytic in the…

We prove that closed manifolds admitting a generic metric whose sectional curvature is locally quasi-constant are graphs of space forms. In the more general setting of QC spaces where sets of isotropic points are arbitrary, under suitable…

We show that pseudovarieties of finitely generated algebras, i.e., classes $C$ of finitely generated algebras closed under finite products, homomorphic images, and subalgebras, can be described via a uniform structure $U$ on the free…

Suppose $G$ is finitely generated group and $\mathcal{C}(G)$ consists of all $\rho:G\to\operatorname{PGL}(n+1,\mathbb{R})$ for which there exists a properly convex set in $\mathbb{R}\mathbb{P}^n$ that is preserved by $\rho(G)$. Then the…

Let $\Gamma$ be a $Q$-polynomial distance-regular graph of diameter $d\geq 3$. Fix a vertex $\gamma$ of $\Gamma$ and consider the subgraph induced on the union of the last two subconstituents of $\Gamma$ with respect to $\gamma$. We prove…

A sequence of graphs with diverging number of nodes is a dense graph sequence if the number of edges grows approximately as for complete graphs. To each such sequence a function, called graphon, can be associated, which contains information…

We give a general construction leading to different non-isomorphic families $\Gamma_{n,q}(\K)$ of connected $q$-regular semisymmetric graphs of order $2q^{n+1}$ embedded in $\PG(n+1,q)$, for a prime power $q=p^h$, using the linear…

Let $G$ be a connected reductive group over a $p$-adic field $F$ of characteristic 0 and let $M$ be an $F$-Levi subgroup of $G.$ Given a discrete series representation $\sigma$ of $M(F),$ we prove that there exists a locally constant and…

Let $G$ be a finite group and let $N$ be a normal subgroup of $G$. We attach to $N$ two graphs ${\Gamma}_G(N)$ and ${\Gamma}^{\ast}_G(N)$ related to the conjugacy classes of $G$ contained in $N$ and to the set of primes dividing the sizes…

We construct homeomorphisms of compacta from relations between finite graphs representing their open covers. Applied to the pseudoarc, this yields simple Fra\"iss\'e theoretic proofs of several important results, both old and new.…

Let $X$ be a real analytic orbifold. Then each stratum of $X$ is a subanalytic subset of $X$. We show that $X$ has a unique subanalytic triangulation compatible with the strata of $X$. We also show that every ${\rm C}^r$-orbifold, $1\leq…

Let $D_j\subset\Bbb C^{k_j}$ be a pseudoconvex domain and let $A_j\subset D_j$ be a locally pluripolar set, $j=1,...,N$. Put$$X:=\bigcup_{j=1}^N A_1\times...\times A_{j-1}\times D_j\times A_{j+1}\times...\times A_N\subset\Bbb…

A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper…

Let $\Gamma$ denote a $Q$-polynomial distance-regular graph with diameter $D\geq 1$. For a vertex $x$ of $\Gamma$ the corresponding subconstituent algebra $T=T(x)$ is generated by the adjacency matrix $A$ of $\Gamma$ and the dual adjacency…

We consider a compact $C^\omega$ manifold $X$ and finitely many regular $C^\omega$ submanifolds $Y_1, \dots, Y_q$ of $X$, which are closed subsets in $X$, such that the union of $Y_j$'s has only normal crossings. We show that every…

Suppose that $\Gamma$ is a non-empty connected graph, $\mathfrak{G}$ is the fundamental group of a graph of groups over $\Gamma$, and $\mathcal{C}$ is a root class of groups (the last means that $\mathcal{C}$ contains non-trivial groups and…