Related papers: Stereographic compactification and affine bi-Lipsc…

We prove that for any non-compact connected surface $M$ the group $H_c(M)$ of compactly suported homeomorphisms of $M$ endowed with the Whitney topology is homeomorphic to $R^\infty\times l_2$ or $Z\times R^\infty\times l_2$.

We give a new proof of a theorem by Le Gall & Paulin, showing that scaling limits of random planar quadrangulations are homeomorphic to the 2-sphere. The main geometric tool is a reinforcement of the notion of Gromov-Hausdorff convergence,…

We discuss the `hd-compactification' of a semi-simple Lie group to a manifold with corners; it is the real analog of the wonderful compactification of deConcini and Procesi. There is a 1-1 correspondence between the boundary faces of the…

Let $X$ be a Banach space or more generally a complete metric space admitting a conical geodesic bicombing. We prove that every closed $L$-Lipschitz curve $\gamma:S^1\rightarrow X$ may be extended to an $L$-Lipschitz map defined on the…

For any $\Lambda>0$, let $\mathcal{M}_{n,\Lambda}$ denote the space containing all locally Lipschitz minimal graphs of dimension $n$ and of arbitrary codimension $m$ in Euclidean space $\mathbb{R}^{n+m}$ with uniformly bounded 2-dilation…

We introduce fibrewise compactifications in both the setting of locally compact Hausdorff spaces and continuous maps, and the parallel setting of $C^*$-algebras and nondegenerate multiplier-valued $*$-homomorphisms. In both situations, we…

After recent work of Hill, Hopkins, and Ravenel on the Kervaire invariant one problem, as well as Adams' solution of the Hopf invariant one problem, an immediate consequence of Curtis conjecture is that the set of spherical classes in…

In this article we explore compactifications of cluster varieties of finite type in complex dimension two. Cluster varieties can be viewed as the spec of a ring generated by theta functions and a compactification of such varieties can be…

We study the local Lipschitz one subsets of a finite dimensional space, that is, sets for which there exists a continuous function whose local Lipschitz derivative is the characteristic function of said set. We give a characterization of a…

For a closed oriented surface $ \Sigma $ we define its degenerations into singular surfaces that are locally homeomorphic to wedges of disks. Let $X_{\Sigma,n}$ be the set of isomorphism classes of orientation preserving $n$-fold branched…

We prove a generalization of the fixed point theorem of Cartwright and Littlewood. Namely, suppose $h : \mathbb{R}^2 \to\mathbb{R}^2$ is an orientation preserving planar homeomorphism, and let $C$ be a continuum such that $h^{-1}(C)\cup C$…

Consider a stratified space with a positive Ricci lower bound on the regular set and no cone angle larger than 2$\pi$. For such stratified space we know that the first non-zero eigenvalue of the Laplacian is larger than or equal to the…

In this article we study minimal homeomorphisms(all orbits are dense) of the tori $T^{n},$ $n<5.$ The linear part of a homeomorphism $\phi $ of $T^{n}$ is the linear mapping $L$ induced by $\phi $ on the first homology group of $T^{n}$. It…

We prove an "abelian, locally compact" Whitehead theorem in fine shape: A fine shape morphism between locally connected finite-dimensional locally compact separable metrizable spaces with trivial $\pi_0$ and $\pi_1$ is a fine shape…

It is known that for every continuous real-valued function $f$ on the circle $\mathbb T=\mathbb R/2\pi\mathbb Z$ there exists a change of variable, i.e., a self-homeomorphism $h$ of $\mathbb T$, such that the superposition $f\circ h$ is in…

The main result states that a connected conic singular sub-manifold of a Riemannian manifold, compact when the ambient manifold is non-Euclidean, is Lipschitz Normally Embedded: the outer and inner metric space structures are metrically…

We study conditions under which a piecewise affine mapping has the Lipschitz shadowing property. As an application, we show that there exists a homeomorphism with a nonisolated fixed point having the Lipschitz shadowing property.

This article deals with directional rotational deviations for non-wandering periodic point free homeomorphisms of the 2-torus which are homotopic to the identity. We prove that under mild assumptions, such a homeomorphism exhibits uniformly…

We define $\partial$-biLipschitz homeomorphisms between uniform metric spaces and show that these maps are always quasim\"obius. We also show that a homeomorphism being $\partial$-biLipschitz is equivalent to the map biLipschitz in the…

Let \Sigma_g be a closed orientable surface let Diff_0(\Sigma_g; area) be the identity component of the group of area-preserving diffeomorphisms of \Sigma_g. In this work we present an extension of Gambaudo-Ghys construction to the case of…