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Master's Dissertation
DOI
https://doi.org/10.11606/D.55.2011.tde-09062011-114204
Document
Author
Full name
Henry José Gullo Mercado
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2011
Supervisor
Committee
Mattos, Denise de (President)
Goncalves, Daciberg Lima
Libardi, Alice Kimie Miwa
 
Title in Portuguese
O anel de cohomologia do espaço de órbitas de Zp -ações livres sobre produtos de esferas
Keywords in Portuguese
Anel de cohomologia
Espaço de órbitas
G-fibrado universal
Produto de esferas
Seqüência espectral
Zp-ações livres
Abstract in Portuguese
Denotemos por X ~ p 'S POT. m' x 'S POT. n' um espaço finitístico com anel de cohomologia módulo p isomorfo ao anel de cohomologia de um produto de esferas 'S POT. m' x 'S POT. n', o qual admite ação livre do grupo cíclico G = Zp, com p um primo ímpar. Nosso objetivo neste trabalho é determinar o anel de cohomologia do espaço de órbitas X / G, usando como ferramenta principal a seqüência espectral de Leray-Serre associada à fibração de Borel X 'SETA' 'imath' X G 'SETA' 'pi' B G, onde BG é o espaço classificante do G-fibrado universal wG = (EG;BG; pG; G;G) e XG = EG x G X é o espaço de Borel. Este resultado foi provado por R. M. Dotzel, T. B. Singh and S. P. Tripathi em [14]
 
Title in English
The cohomology rings of the orbit spaces of Zp-free transformation groups of the product of two spheres
Keywords in English
. Orbit spaces
Cohomology rings
Product of two spheres
Spectral sequence
Universal G-Bundle
Zp-free actions
Abstract in English
Let denote by X ~ p 'S POT. m' x 'S POT. n' finitistic space with mod p cohomology ring isomorphic to the cohomology ring of a product of spheres 'S POT. m' x 'S POT. n' , which admits a free action of the cyclic group G = Zp, with p an odd prime. Our goal in this work is to determine the cohomology ring of the orbit space X / G, using as main tool the Leray-Serre spectral sequence associated to the Borel fibration X 'SETA" 'imath' 'X G 'SETA' 'pi' BG, where BG is the classifying space of the G-universal bundle wG = (EG;BG; pG; G;G) and XG = EG x G X is the Borel space. This result was proved by R. M. Dotzel, T. B. Singh and S. P. Tripathi in [14]
 
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Publishing Date
2011-06-09
 
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