Reversibility properties of semigroup actions on homogeneous spaces

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Curves in homogeneous spaces and their contact with 1-dimensional orbits

Let alpha be a C(infinity) curve in a homogeneous space G/H. For each point x on the curve, we consider the subspace S(k)(alpha) of the Lie algebra G of G consisting of the vectors generating a one parameter subgroup whose orbit through x has contact of order k with alpha. In this paper, we give various important properties of the sequence of subspaces G superset of S(1)(alpha) superset of S(2)(alpha) superset of S(3)(alpha) superset of ... In particular, we give a stabilization property for certain well-behaved curves. We also describe its relationship to the isotropy subgroup with respect to the contact element of order k associated with alpha.

About Homogeneous Spaces and Conditions of Completeness of Spaces

Александър В. Архангелски, Митрофан М. Чобан, Екатерина П. Михайлова - Въведени са понятията o-хомогенно пространство, lo-хомогенно пространство, do-хомогенно пространство и co-хомогенно пространство. Показано е, че ако lo-хомогенно пространство X има отворено подпространство, което е q-пълно, то и самото X е q-пълно. Показано е, че ако lo-хомогенно пространство X съдържа навсякъде гъсто екстремално несвързано подпространство, тогава X е екстремално несвързано.

About Homogeneous Spaces and the Baire Property in Remainders

Александър В. Архангелски, Митрофан М. Чобан, Екатерина П. Михайлова - В съобщението е продължено изследването на понятията o-хомогенно пространство, lo-хомогенно пространство, do-хомогенно пространство и co-хомогенно пространство. Показано е, че ако co-хомогенното пространство X съдържа Gδ -гъсто Московско подпространство, тогава X е Московско пространство.

On a Gromoll-Meyer type theorem in globally hyperbolic stationary spacetimes

Following the lines of the celebrated Riemannian result of Gromoll and Meyer, we use infinite dimensional equivariant Morse theory to establish the existence of infinitely many geometrically distinct closed geodesics in a class of globally hyperbolic stationary Lorentzian manifolds.

Equivariant Nielsen root theory for G-maps

Let X be a compact Hausdorff space, Y be a connected topological manifold, f : X -> Y be a map between closed manifolds and a is an element of Y. The vanishing of the Nielsen root number N(f; a) implies that f is homotopic to a root free map h, i.e., h similar to f and h(-1) (a) = empty set. In this paper, we prove an equivariant analog of this result for G-maps between G-spaces where G is a finite group. (C) 2010 Elsevier B.V. All rights reserved.

Região, território e planejamento estatal: planejamento plurianual e desenvolvimento regional

O presente trabalho tem a intenção de analisar as discussões em torno da dimensão territorial no planejamento estatal. Essas discussões não são recentes, elas emergiram no cenário nacional em decorrência também das questões relacionadas a um conjunto de fatores que surgem como imposição do processo de acumulação flexível e globalizado, que busca produzir espaços homogêneos. Nesse momento o próprio papel do Estado, enquanto promotor do desenvolvimento é redefinido, alterando assim, sua relação de poder na produção do espaço, estabelecendo com isso, uma correlação de força com a sociedade. Todavia as questões que envolvem o planejamento recente no Brasil passam pela resolução de pontos cruciais, que estão diretamente ligadas às estratégias de intervenção do Estado a partir de uma lógica territorializada, que em primeiro lugar tem a região como ponto de partida. Nessa perspectiva se faz necessário pensar conceito de região e de território inseridos na dinâmica de planejamento territorial/regional. A tese apresentada neste trabalho demonstra que mesmo havendo um intenso esforço na elaboração dos PPAs e, consequentemente, dos planos e programas a eles ligados, no que se refere à introdução de um “moderno” planejamento público, a partir da introdução da concepção de território e demais instrumentos de execução e avaliação, quando se analisa o orçamento-programa percebe-se que os mesmos seguem outra lógica regionalizada de alocação de recursos, obedecendo a Constituição Federal, tanto no que se refere aos programas finalísticos, quanto ao de apoio às políticas públicas e áreas especiais. Assim, o orçamento segue uma dinâmica regionalizada, enquanto os planos e programas seguem uma dinâmica territorial. Enquanto o orçamento-programa estabelece a alocação de recursos seguindo o critério de divisão regional do IBGE – que divide o Brasil em cinco regiões. Os estudos da Dimensão Territorial para o Planejamento que orientam os PPAs, destacando, principalmente o 2008 – 2011 buscam estabelecer programas de desenvolvimento a partir da criação de inúmeros territórios. Passando assim, a desenvolver um sério problema na dinâmica do planejamento público brasileiro, que é o descompasso entre Plano – Orçamento – Programa, negando, com isso, a concepção de integração presente nos mesmos.

On the Factorization of the Poincaré Polynomial: A Survey

2000 Mathematics Subject Classification: 13P05, 14M15, 14M17, 14L30.

Absolutely Continuous Spectrum for Parabolic Flows/Maps

This work is devoted to creating an abstract framework for the study of certain spectral properties of parabolic systems. Specifically, we determine under which general conditions to expect the presence of absolutely continuous spectral measures. We use these general conditions to derive results for spectral properties of time-changes of unipotent flows on homogeneous spaces of semisimple groups regarding absolutely continuous spectrum as well as maximal spectral type; the time-changes of the horocycle flow are special cases of this general category of flows. In addition we use the general conditions to derive spectral results for twisted horocycle flows and to rederive spectral results for skew products over translations and Furstenberg transformations.

Global, Local and Vector-Valued Tb Theorems on Non-Homogeneous Metric Spaces

Various Tb theorems play a key role in the modern harmonic analysis. They provide characterizations for the boundedness of Calderón-Zygmund type singular integral operators. The general philosophy is that to conclude the boundedness of an operator T on some function space, one needs only to test it on some suitable function b. The main object of this dissertation is to prove very general Tb theorems. The dissertation consists of four research articles and an introductory part. The framework is general with respect to the domain (a metric space), the measure (an upper doubling measure) and the range (a UMD Banach space). Moreover, the used testing conditions are weak. In the first article a (global) Tb theorem on non-homogeneous metric spaces is proved. One of the main technical components is the construction of a randomization procedure for the metric dyadic cubes. The difficulty lies in the fact that metric spaces do not, in general, have a translation group. Also, the measures considered are more general than in the existing literature. This generality is genuinely important for some applications, including the result of Volberg and Wick concerning the characterization of measures for which the analytic Besov-Sobolev space embeds continuously into the space of square integrable functions. In the second article a vector-valued extension of the main result of the first article is considered. This theorem is a new contribution to the vector-valued literature, since previously such general domains and measures were not allowed. The third article deals with local Tb theorems both in the homogeneous and non-homogeneous situations. A modified version of the general non-homogeneous proof technique of Nazarov, Treil and Volberg is extended to cover the case of upper doubling measures. This technique is also used in the homogeneous setting to prove local Tb theorems with weak testing conditions introduced by Auscher, Hofmann, Muscalu, Tao and Thiele. This gives a completely new and direct proof of such results utilizing the full force of non-homogeneous analysis. The final article has to do with sharp weighted theory for maximal truncations of Calderón-Zygmund operators. This includes a reduction to certain Sawyer-type testing conditions, which are in the spirit of Tb theorems and thus of the dissertation. The article extends the sharp bounds previously known only for untruncated operators, and also proves sharp weak type results, which are new even for untruncated operators. New techniques are introduced to overcome the difficulties introduced by the non-linearity of maximal truncations.