Related papers: Cycle Connectivity and Automorphism Groups of Flag…

Let $D=\{\rho < 0\}$ be a smooth relatively compact domain in an almost complex manifold $(M,J)$, where $\rho$ is a smooth defining function of $D$, strictly $J$-plurisubharmonic in a neighborhood of the closure $\overline{D}$ of $D$. We…

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…

We show that, inside the Shilov boundary of any given Hermitian symmetric space of tube type, there is, up to isomorphism, only one proper domain such that every point on its boundary belongs to the closure of an orbit under its…

Let D be a relatively compact strongly pseudoconvex domain in a Stein manifold, and let Y be a complex manifold. We prove that the set A(D,Y), consisting of all continuous maps from the closure of D to Y which are holomorphic in D, is a…

We prove that Ad-semisimple conjugacy classes in a connected Lie group $G$ are closed embedded submanifolds of $G$. We also prove that if $\alpha:H\to G$ is a homomorphism of connected Lie groups such that the kernel of $\alpha$ is discrete…

Let $\Phi$ be a pseudo-Anosov diffeomorphism of a compact (possibly non-orientable) surface $\Sigma$ with one boundary component. We show that if $b \in \pi_1(\Sigma)$ is the boundary word, $\phi \in {\rm{Aut}}(\pi_1(\Sigma))$ is a…

Let $R$ be a commutative ring with identity. We define a graph $\Gamma_{\aut}(R)$ on $ R$, with vertices elements of $R$, such that any two distinct vertices $x, y$ are adjacent if and only if there exists $\sigma \in \aut$ such that…

Assume that $X$ and $Y$ are arithmetic schemes, i.e., integral schemes of finite types over $Spec(\mathbb{Z})$. Then $X$ is said to be quasi-galois closed over $Y$ if $X$ has a unique conjugate over $Y$ in some certain algebraically closed…

We study the automorphisms group action on a bounded domain in $\CC^n$ having a boundary point that is exponentially flat. Such a domain typically has a compact automorphism group. Our results enable us to generate many new examples.

Let D be a bounded strongly pseudoconvex domain in a Stein manifold S and let Y be a complex manifold. We prove that the graph of any continuous map from the closure of D to Y which is holomorphic in D admits a basis of open Stein…

In this paper, we study conditions which ensure the existence of backward flow invariant domains for semigroups of holomorphic self-mappings of a simply connected domain $D$. More precisely, the problem is the following. Given a…

For a compact Lie group $G$ with maximal torus $T$, Pittie and Smith showed that the flag variety $G/T$ is always a stably framed boundary. We generalize this to the category of $p$-compact groups, where the geometric argument is replaced…

Let $P=G/K$ be a semisimple non-compact Riemannian symmetric space, where $G=I_0(P)$ and $K=G_p$ is the stabilizer of $p\in P$. Let $X$ be an orbit of the (isotropy) representation of $K$ on $T_p(P)$ ($X$ is called a real flag manifold).…

In contrast to the many examples of convex divisible domains in real projective space, we prove that up to projective isomorphism there is only one convex divisible domain in the Grassmannian of $p$-planes in $\mathbb{R}^{2p}$ when $p > 1$.…

A flag manifold over a semifield K can be partitioned into "half i-circles" which are orbits of a K-action on that flag manifold. Here i is fixed and it corresponds to a simple reflection in the Weyl group. We prove (for certain K) a…

Let $M$ be a closed connected smooth manifold and $G=\textmd{Diff}_0(M)$ denote the connected component of the diffeomorphism group of $M$ containing the identity. The natural action of $G$ on $M$ induces the trace homomorphism on homology.…

Let $D$ be a bounded homogeneous domain in $\mbb{C}^n$ and let $\Gamma$ be a cyclic discrete subgroup of the automorphism group of $D$. It is shown that the complex space $D/\Gamma$ is Stein.

We prove that any coadjoint orbit with real eigenvalues of a complex semisimple Lie group, equipped with the real part of the canonical holomorphic symplectic form, is symplectomorphic to the cotangent bundle of a (partial) flag manifold.…

In 1992, David Wright proved a remarkable theorem about which contractible open manifolds are covering spaces. He showed that if a one-ended open manifold M has pro-monomorphic fundamental group at infinity which is not pro-trivial and is…

The Diederich-Forn{\ae}ss worm domain, an important example of a smoothly bounded pseudoconvex domain without a Stein neighborhood basis, provides key counterexamples in the theory of Several Complex Variables. In this paper, we examine its…