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Master's Dissertation
Document
Author
Full name
Francisco Dutenhefner
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1996
Supervisor
Committee
Vergara, Jose Luis Arraut (President)
Daccach, Janey Antonio
Saldanha, Nicolau Corção
Title in Portuguese
AÇÕES DE RN SOBRE TN-FRIBRAÇÕES.
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Seja X um fibrado diferenciável com fibra típica o toro Tn sobre urna variedade compacta e conexa Mm. Como as órbitas compactas de urna ação localmente livre de Rn são toros, é natural perguntar se existe uma ação localmente livre de Rn em X com órbitas iguais as fibras. No artigo original [23], Nicolau Saldanha estudou este problema e apresentou condições necessárias e suficientes para a existência de uma tal ação. Ele também demonstrou que a desejada ação existe se X e M são orientáveis, n ≤ 2 e m ≤ 2 mas pode não existir se qualquer urna destas três hipóteses é retirada. Este artigo é o objeto do nosso estudo. Aqui, apresentamos urna detalhada exposição dos conteúdos deste artigo.
Title in English
Not available
Keywords in English
Not available
Abstract in English
Let X be a smooth fibre bundle with typical fibre the torus Tn over a smooth compact connected manifold Mm. Since the compact orbits of an locally free action of Rn are tori it is natural to ask if there exists a smooth locally free action of Rn over X with orbits equal to the fibres. In the original paper [23], Nicolau Saldanha studied this problem and gave necessary and sufficient conditions for the existence of such an action. He also proved that the desired action exists if X and M are orientable, n ≤ 2 and m ≤ 2 but may not exist if any of this three conditions is dropped. This paper was the object of our study. Here, we make a detailed exposition of the contents of this paper.
 
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Publishing Date
2018-01-12
 
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