Equivariant maps of -actions into polyhedra
On présente dans cet exposé une approche semi-classique déduite des résultats de N. Burq, P. Gérard et N. Tzvetkov [4] permettant de démontrer des inégalités de Strichartz pour un problème non captif. On retrouve ainsi des résultats de G. Staffilani et D. Tataru [16] (obtenus pour une perturbation de la métrique à support compact). On donne aussi des généralisations de ces résultats au cas d’une perturbation à longue portée
Continuing studies on 2-to-1 maps onto indecomposable continua having only arcs as proper non-degenerate subcontinua - called here arc-continua - we drop the hypothesis of tree-likeness, and we get some conditions on the arc-continuum image that force any 2-to-1 map to be a local homeomorphism. We show that any 2-to-1 map from a continuum onto a local Cantor bundle Y is either a local homeomorphism or a retraction if Y is orientable, and that it is a local homeomorphism if Y is not orientable.
It is known that no dendrite (Gottschalk 1947) and no hereditarily indecomposable tree-like continuum (J. Heath 1991) can be the image of a continuum under an exactly 2-to-1 (continuous) map. This paper enlarges the class of tree-like continua satisfying this property, namely to include those tree-like continua whose nondegenerate proper subcontinua are arcs. This includes all Knaster continua and Ingram continua. The conjecture that all tree-like continua have this property, stated by S. Nadler...