相关论文: On epimorphisms in some categories of infinite-dim…

The article is devoted to the investigation of groups of diffeomorphisms and loops of manifolds over ultra-metric fields of zero and positive characteristics. Different types of topologies are considered on groups of loops and…

Let $X$ be a differentiable manifold endowed with a transitive action $\alpha:A\times X\longrightarrow X$ of a Lie group $A$. Let $K$ be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms…

Suppose $G$ is a connected complex Lie group and $\Gamma$ is a discrete subgroup such that $X := G/\Gamma$ is K\"ahler and the codimension of the top non--vanishing homology group of $X$ with coefficients in $\mathbb Z_2$ is less than or…

We study the relation between two special classes of Riemannian Lie groups $G$ with a left-invariant metric $g$: The Einstein Lie groups, defined by the condition $\operatorname{Ric}_g=cg$, and the geodesic orbit Lie groups, defined by the…

An infra-nilmanifold is a manifold which is constructed as a quotient space $\Gamma\backslash G$ of a simply connected nilpotent Lie group $G$, where $\Gamma$ is a discrete group acting properly discontinuously and cocompactly on $G$ via so…

Let G be a Lie group and E be a locally convex topological G-module. If E is sequentially complete, then E and its space of smooth vectors are modules for the algebra D(G) of compactly supported smooth functions on G. However, the module…

Given a compact Lie group $G$, a reconstruction theorem for free $G$-manifolds is proved. As a by-product reconstruction results for locally trivial bundles are presented. Next, the main theorem is generalized to $G$-manifolds with one…

Let $G$ be a locally convex Lie group and $\pi:G \to \mathrm{U}(\mathcal{H})$ be a continuous unitary representation. $\pi$ is called smooth if the space of $\pi$-smooth vectors $\mathcal{H}^\infty\subset \mathcal{H}$ is dense. In this…

We show that in the presence of suitable commutator estimates, a projective unitary representation of the Lie algebra of a connected and simply connected Lie group G exponentiates to G. Our proof does not assume G to be finite--dimensional…

Let G be a connected complex simple Lie group with maximal compact subgroup U. Let g be the Lie algebra of G, and X = G/U be the associated Riemannian globally symmetric space of type IV. We have constructed three types of arithmetic…

We define submersions f between manifolds M and N modelled on locally convex spaces. If the range N is finite-dimensional or a Banach manifold, then these coincide with the naive notion of a submersion. We study pre-images of submanifolds…

For a Lie group $G$ and a closed Lie subgroup $H\subset G$, it is well known that the coset space $G/H$ can be equipped with the structure of a manifold homogeneous under $G$ and that any $G$-homogeneous manifold is isomorphic to one of…

Consider the real free Lie algebra $\mathfrak{fr}_n$ with generators $\omega_1$, \dots, $\omega_n$. Since it is positively graded, it has a completion $\overline{\mathfrak{fr}}_n$ consisting of formal series. By the Campbell--Hausdorff…

Let $\varphi$ and $\varphi'$ be two homotopic actions of the topological group $G$ on the topological space $X$. To an object $A$ in the $G$-equivariant derived category $D_{\varphi}(X)$ of $X$ relative to the action $\varphi$ we associate…

The epireflective subcategories of ${\bold{Top}}$, that are closed under epimorphic (or bimorphic) images, are $\{X \mid |X| \le 1 \} $, $\{X \mid X$ is indiscrete$\} $ and ${\bold{Top}}$. The epireflective subcategories of…

Let $G$ be a compact Lie group acting effectively by isometries on a compact Riemannian manifold $M$ with nonempty fixed point set $Fix(M,G)$. We say that the action is \emph{fixed point homogeneous} if $G$ acts transitively on a normal…

For a compact, smooth C^r orbifold (without boundary), we show that the topological structure of the orbifold diffeomorphism group is a Banach manifold for finite r \ge 1 and a Frechet manifold if r=infty. In each case, the local model is…

Let $B$ be Banach algebra and $M$ be topological space. If there exists homeomorphism \[ f:M\rightarrow N \] of topological space $M$ into convex set $N$ of the space $B^n$, then homeomorphism $f$ is called chart of the set $M$. The set $M$…

It has been proved by the author [arXiv: 2404.19433] that the Arens-Michael envelope of a solvable Lie algebra is a homological epimorphism. We show here that for algebras of analytic functionals on a connected complex Lie group the…

Given a closed, smooth 4-manifold $X$ and self-diffeomorphism $f$ that is topologically pseudo-isotopic to the identity, we study the question of whether $f$ is moreover smoothly pseudo-isotopic to the identity. If the fundamental group of…