Related papers: The space of properly-convex structures

Let $P$ be a set of $n$ points in general position on the plane. A set of closed convex polygons with vertices in $P$, and with pairwise disjoint interiors is called a convex decomposition of $P$ if their union is the convex hull of $P$,…

Let G be a finite group acting tamely on a proper reduced curve C over an algebraically closed field. We study the G-module structure on the cohomology groups of a G-equivariant locally free sheaf F on C, and give formulas of…

To any dg-category $T$ (over some base ring $k$), we define a $D^{-}$-stack $\mathcal{M}_{T}$ in the sense of \cite{hagII}, classifying certain $T^{op}$-dg-modules. When $T$ is saturated, $\mathcal{M}_{T}$ classifies compact objects in the…

An $integral$ of a group $G$ is a group $H$ whose derived group (commutator subgroup) is isomorphic to $G$. This paper discusses integrals of groups, and in particular questions about which groups have integrals and how big or small those…

Let $(X,T^{1,0}X)$ be a $(2n+1+d)$-dimensional compact CR manifold with codimension $d+1$, $d\geq1$, and let $G$ be a $d$-dimensional compact Lie group with CR action on $X$ and $T$ be a globally defined vector field on $X$ such that…

The main theorem shows that if M is an irreducible compact connected orientable 3-manifold with non-empty boundary, then the classifying space BDiff(M rel dM) of the space of diffeomorphisms of M which restrict to the identity map on…

Let M and N be even-dimensional oriented real manifolds, and $u:M \to N$ be a smooth mapping. A pair of complex structures at M and N is called u-compatible if the mapping u is holomorphic with respect to these structures. The quotient of…

Let $\mc G$ be a reductive group over an algebraically closed field of characteristic $p>0$. We study homogeneous $\mc G$-spaces that are induced from the $G\times G$-space $G$, $G$ a suitable reductive group, along a parabolic subgroup of…

We prove several results of the following type: given finite dimensional normed space V possessing certain geometric property there exists another space X having the same property and such that (1) log (dim X) = O(log (dim V)) and (2) every…

We show that compact complex manifolds of algebraic dimension zero bearing a holomorphic Cartan geometry of algebraic type have infinite fundamental group. This generalizes the main Theorem in [DM] where the same result was proved for the…

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…

We introduce the space of infinite volume ends of a locally compact second countable (lcsc) space that admits a Radon measure. In certain cases, this coincides with the classical space of ends. Consider a discrete subgroup $\Gamma$ of a…

If H is a flat group of automorphisms of finite rank n of a totally disconnected, locally compact group G, then each orbit of H in the metric space B(G) of compact, open subgroups of G is quasi-isometric to n-dimensional euclidean space. In…

Let $G$ be a locally compact group. Then for every $G$-space $X$ the maximal $G$-proximity $\beta_G$ can be characterized by the maximal topological proximity $\beta$ as follows: $$ A \ \overline{\beta_G} \ B \Leftrightarrow \exists V \in…

A real projective orbifold is an $n$-dimensional orbifold modeled on $\mathbb{RP}^n$ with the group $PGL(n+1, \mathbb{R})$. We concentrate on an orbifold that contains a compact codimension $0$ submanifold whose complement is a union of…

We introduce a new class of locally compact groups, namely the strongly compactly covered groups, which are the Hausdorff topological groups $G$ such that every element of $G$ is contained in a compact open normal subgroup of $G$. For…

Let $M$ be a commutative homogeneous space of a compact Lie group $G$ and $A$ be a closed $G$-invariant subalgebra of the Banach algebra $C(M)$. A function algebra is called antisymmetric if it does not contain nonconstant real functions.…

Let X be a locally compact Polish space and G a non-discrete Polish ANR group. By C(X,G), we denote the topological group of all continuous maps f:X \to G endowed with the Whitney (graph) topology and by C_c(X,G) the subgroup consisting of…

Consider a finite dimensional (generally reducible) polynomial representation \rho of GL_n. A projective compactification of GL_n is the closure of \rho(GL_n) in the space of all operators defined up to a factor (this class of spaces can be…

Let $X \subset \mathbb{C}^n$ be an algebraic variety, and let $\Lambda \subset \mathbb{C}^n$ be a discrete subgroup whose real and complex spans agree. We describe the topological closure of the image of $X$ in $\mathbb{C}^n / \Lambda$,…