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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...

Grafting Seiberg-Witten monopoles.

Jabuka, Stanislav (2003)

Algebraic & Geometric Topology

Graphs and projective planes in 3-manifolds.

Heil, Wolfgang, Negami, Seiya (1986)

International Journal of Mathematics and Mathematical Sciences

Group actions on fibered three-manifolds.

Allan L. Edmonds, Charles Livingston (1983)

Commentarii mathematici Helvetici

Group Actions on the Chern Manifold.

Dariusz M. Wilcznski (1988)

Mathematische Annalen

Group negative curvature for 3-manifolds with genuine laminations.

Gabai, David, Kazez, William H. (1998)

Geometry & Topology

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...

Groupoids, the Phragmen-Brouwer property, and the Jordan curve theorem.

Brown, Ronald (2006)

Journal of Homotopy and Related Structures

Groups acting on $CAT (0)$ cube complexes.

Niblo, Graham, Reeves, Lawrence (1997)

Geometry & Topology

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.

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