We prove that manifolds with complicated enough fundamental group admit measure-preserving homeomorphisms which have positive stable fragmentation norm respect to balls of bounded measure.

Ordered sheaves on a small quantaloid Q have been defined in terms of Qenriched categorical structures; they form a locally ordered category Ord(Q). The free-cocompletion KZ-doctrine on Ord(Q) has Mod(Q), the quantaloid of Q-modules, as category of Eilenberg-Moore algebras. In this paper we give an intrinsic description of the Kleisli algebras: we call them the locally principally generated Q-m...

Such a space is unique up to isometry. We shall investigate group LIP(U) of bilipschitz homeomorphisms of U and some related groups. Indeed, the group H(U) of all homeomorphisms of U comes to mind first. However, by V. Uspenskiy [Us], U is homeomorphic to l2. So H(U) is in fact the group of homeomomorphisms of a Banach space, and can be better understood as such. For LIP(U) and for other groups...

Let Hg be a genus g handlebody and MCG2n(Tg) be the group of the isotopy classes of orientation preserving homeomorphisms of Tg = ∂Hg, fixing a given set of 2n points. In this paper we find a finite set of generators for E 2n, the subgroup of MCG2n(Tg) consisting of the isotopy classes of homeomorphisms of Tg admitting an extension to the handlebody and keeping fixed the union of n disjoint pro...

Abstract We discuss the question of extending homeomorphisms between closed subsets Cantor cube $D^{\tau }$ . It is established that any homeomorphism two negligible can be extended to an autohomeomorphism

In this paper we primarily consider two natural subgroups of the autohomeomorphism group of the real line R, endowed with the compact-open topology. First, we prove that the subgroup of homeomorphisms that map the set of rational numbers Q onto itself is homeomorphic to the infinite power of Q with the product topology. Secondly, the group consisting of homeomorphisms that map the pseudoboundar...

This is the announcement, and the long summary, of a series of articles on the algorithmic study of Thurston maps. We describe branched coverings of the sphere in terms of group-theoretical objects called bisets, and develop a theory of decompositions of bisets. We introduce a canonical “Levy” decomposition of an arbitrary Thurston map into homeomorphisms, metrically-expanding maps and maps dou...

We give a parametrization of the asymptotic Teichmüller space AT (D) of the open unit disk through a space of equivalent classes of the shear functions induced by quasisymmetric homeomorphisms on the Farey tesselation of the disk. Then using the parametrization, we define a metric on AT (D). Two other related metrics are also introduced on AT (D) by using cross-ratio distortions or quadrilatera...

We continue the description of Mandelbrot and Multibrot sets and of Julia sets in terms of fibers which was begun in [S3] and [S4]. The question of local connectivity of these sets is discussed in terms of fibers and becomes the question of triviality of fibers. In this paper, the focus is on the behavior of fibers under renormalization and other surgery procedures. We show that triviality of f...

We study homeomorphisms h : X onto −→ Y between two bounded domains in Rn having finite conformal energy E[h] = ∫ X ||Dh(x) || n dx < ∞ , h ∈ W (X,Y). We consider the behavior of such mappings, including continuous extension to the closure of X and injectivity of h : X → Y. In general, passing to the weak W 1,n-limit of a sequence of homeomorphisms hj : X → Y one loses injectivity. However, if ...