Related papers: Homeomorphisms of the Pseudoarc
This paper deals with the problem of conjugacy of Cartan subalgebras for affine Kac-Moody Lie algebras. Unlike the methods used by Peterson and Kac, our approach is entirely cohomological and geometric. It is deeply rooted on the theory of…
In this work, we study direct limits of finite dimensional basic classical simple Lie superalgebras and obtain the conjugacy classes of Cartan subalgebras under the group of automorphisms.
For any Tychonoff space $X$ let $C_p(X)$ (resp., $C^*_p(X)$) be the set of all continuous (resp., and bounded) functions on $X$ with the pointwise convergence topology. Given Tychonoff spaces $X$ and $Y$, Uspenskij \cite{us} proved that if…
We develop a class of homeomorphisms on a compact homogeneous space of a transitive group action and show how the class sheds new light on a decomposition problem. We further use this class to show that every such homogeneous space in a…
We introduce and study the framework of compact metric structures and their associated notions of isomorphisms such as homeomorphic and bi-Lipschitz isomorphism. This is subsequently applied to model various classification problems in…
Consider a sequence of compactly supported Hamiltonian diffeomorphisms $\phi_k$ of an exact symplectic manifold, all of which are "graphical" in the sense that their graphs are identified by a Darboux-Weinstein chart with the image of a…
Separately continuous bihomomorphisms on a product of convergence or topological groups occur with great frequency. Of course, in general, these need not be jointly continuous. In this paper, we exhibit some results of Banach-Steinhaus type…
The classifying spaces of cobordisms of singular maps have two fairly different constructions. We expose a homotopy theoretical connection between them. As a corollary we show that the classifying spaces in some cases have a simple product…
We develop the theory of locally analytic representations of compact $p$-adic Lie groups from the perspective of the theory of condensed mathematics of Clausen and Scholze. As an application, we generalise Lazard's isomorphisms between…
This survey describes some useful properties of the local homology of abstract simplicial complexes. Although the existing literature on local homology is somewhat dispersed, it is largely dedicated to the study of manifolds, submanifolds,…
This self-contained paper is part of a series \cite{FF2,FF3} on actions by diffeomorphisms of infinite groups on compact manifolds. The two main results presented here are: 1) Any homomorphism of (almost any) mapping class group or…
We study the topological structure of the automorphism groups of compact quantum groups showing that, in parallel to a classical result due to Iwasawa, the connected component of identity of the automorphism group and of the "inner"…
We reduce the classification of finite subgroups in compact Lie groups to that of quasi-simple ones, prove the number of conjugacy classes is finite and each cojugacy class is Zariski closed in mapping space, and classify "strongly…
A digraph is connected-homogeneous if any isomorphism between finite connected induced subdigraphs extends to an automorphism of the digraph. We consider locally-finite connected-homogeneous digraphs with more than one end. In the case that…
We discuss some notions of compactness and convergence relative to a specified family F of subsets of some topological space X. The two most interesting particular cases of our construction appear to be the following ones. (1) The case in…
In this article we characterize monotone extensions of cw-expansive homeomorphisms of compact metric spaces. We study the topology of its quotient space in the case of a compact surface. These results are applied to prove that there are…
Without leaving finite mathematics and using finite topological spaces only, we give a definition of homeomorphisms of finite abstract simplicial complexes or finite graphs. Besides exploring the definition in various contexts, we add some…
In this paper, we investigate a family of graphs associated to collections of arcs on surfaces. These {\it multiarc graphs} naturally interpolate between arc graphs and flip graphs, both well studied objects in low dimensional geometry and…
In this paper, we present a $C^0$-fragmentation property for Hamiltonian diffeomorphisms. More precisely, it is known that for a given open covering $\mathcal{U}$ of a compact symplectic surface we can write each $C^0$-small enough…
We prove a topological rigidity result for simple, thick, hyperbolic P-manifolds of dimension 2: isomorphism of the fundamental groups implies homeomorphism of the P-manifolds. An immediate application is a diagram rigidity theorem for…