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Doctoral Thesis
DOI
10.11606/T.45.2019.tde-18032019-195116
Document
Author
Full name
Renato Vasconcellos Vieira
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2018
Supervisor
Committee
Goncalves, Daciberg Lima (President)
Barros, Tomas Edson
Hoefel, Eduardo Outeiral Correa
Jardim, Marcos Benevenuto
Manzoli Neto, Oziride
Title in Portuguese
Princípio de reconhecimento de espaços de laços relativos
Keywords in Portuguese
2-operads
Espaços de laços
Espaços de laços relativos
Espectros
Espectros relativos
Operads
Princípio de reconhecimento
Princípio de reconhecimento relativo
Abstract in Portuguese
O princípio de reconhecimento de espaços de $\infty$-laços é que o funtor $\Omega^\infty:\textttightarrow \mathcal E^\infty[\texttt]$ dado por $\Omega^\infty Y_\bullet=\text_{\bullet\shortrightarrow\infty}\Omega^\bullet Y_\bullet$ induz uma equivalência entre a categoria homotópica de espectros conectivos e a categoria homotópica de $\mathcal E^\infty$-álgebras grouplike para qualquer resolução cofibrante $\mathcal E^\infty$ do operad $\mathcal Com$ de monóides comutativos. Nesta tese é provado um princípio de reconhecimento de 2-espaços de $N$-laços para $2
Title in English
Recognition principle of relative loop spaces
Keywords in English
2-operads
Loop spaces
Operads
Recognition principle
Relative loop spaces
Relative recognition principle
Relative spectra
Spectra
Abstract in English
The recognition principle of $\infty$-loop spaces is that the functor $\Omega^\infty:\textttightarrow \mathcal E^\infty[\texttt]$ defined by $\Omega^\infty Y_\bullet=\text_{\bullet\shortrightarrow\infty}\Omega^\bullet Y_\bullet$ induces an equivalence between the homotopy category of connective spectra and the homotopy category of grouplike $\mathcal E^\infty$-algebras for any cofibrant resolution $\mathcal E^\infty$ of the commutative monoid operad $\mathcal Com$. In this thesis a relative recognition principle of $N$-loop 2-spaces is proved for $2
 
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TeseRenatoVVieira.pdf (864.42 Kbytes)
Publishing Date
2019-03-26
 
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