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Good metric spaces without good parameterizations.

Stephen Semmes (1996)

Revista Matemática Iberoamericana

A classical problem in geometric topology is to recognize when a topological space is a topological manifold. This paper addresses the question of when a metric space admits a quasisymmetric parametrization by providing examples of spaces with many Eucledian-like properties which are nonetheless substantially different from Euclidean geometry. These examples are geometrically self-similar versions of classical topologically self-similar examples from geometric topology, and they can be realized...

Groupes fondamentaux des variétés de dimension 3 et algèbres d’opérateurs

Pierre de la Harpe, Jean-Philippe Préaux (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

Nous proposons une caractérisation géométrique des variétés de dimension  3 ayant des groupes fondamentaux dont toutes les classes de conjugaison autres que  { 1 } sont infinies, c’est-à-dire dont les algèbres de von Neumann sont des facteurs de type  I I 1   : ce sont essentiellement les 3 -variétés à groupes fondamentaux infinis qui n’admettent pas de fibration de Seifert. Autrement dit et plus précisément, soient  M une 3 -variété connexe compacte et Γ son groupe fondamental, qu’on suppose être infini et avec...

Group-theoretic conditions under which closed aspherical manifolds are covered by Euclidean space

Hanspeter Fischer, David G. Wright (2003)

Fundamenta Mathematicae

Hass, Rubinstein, and Scott showed that every closed aspherical (irreducible) 3-manifold whose fundamental group contains the fundamental group of a closed aspherical surface, is covered by Euclidean space. This theorem does not generalize to higher dimensions. However, we provide geometric tools with which variations of this theorem can be proved in all dimensions.

Harmonic morphisms and circle actions on 3- and 4-manifolds

Paul Baird (1990)

Annales de l'institut Fourier

Harmonic morphisms are considered as a natural generalization of the analytic functions of Riemann surface theory. It is shown that any closed analytic 3-manifold supporting a non-constant harmonic morphism into a Riemann surface must be a Seifert fibre space. Harmonic morphisms ϕ : M → N from a closed 4-manifold to a 3-manifold are studied. These determine a locally smooth circle action on M with possible fixed points. This restricts the topology of M . In all cases, a harmonic morphism ϕ : M → N from a closed...

h-cobordism and s-cobordism Theorems: Transfer over Semialgebraic and Nash Categories, Uniform bound and Effectiveness

Mady Demdah Kartoue (2011)

Annales de l’institut Fourier

The h-cobordism theorem is a noted theorem in differential and PL topology. A generalization of the h-cobordism theorem for possibly non simply connected manifolds is the so called s-cobordism theorem. In this paper, we prove semialgebraic and Nash versions of these theorems. That is, starting with semialgebraic or Nash cobordism data, we get a semialgebraic homeomorphism (respectively a Nash diffeomorphism). The main tools used are semialgebraic triangulation and Nash approximation.One aspect of...

Currently displaying 441 – 460 of 1237