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Doctoral Thesis
DOI
Document
Author
Full name
Rafael Moreira de Souza
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2014
Supervisor
Committee
Wong, Peter Ngai Sing (President)
Goncalves, Daciberg Lima
Monis, Thais Fernanda Mendes
Silva, Weslem Liberato
Vendruscolo, Daniel
Title in Portuguese
Realização de conjunto de pontos fixos numa dada classe de homotopia equivariante de aplicações
Keywords in Portuguese
Topologia algébrica
Abstract in Portuguese
Nesse trabalho combinamos a teoria de Nielsen de pontos fixos com a teoria dos grupos de transformações para dar condições necessárias e sucientes para realizar um subconjunto A localmente contrátil de X G - como o conjunto de pontos xos de uma apli- h : X X em uma classe de homotopia equivariante dada, onde G é X é uma G -variedade suave e compacta. Além disso, se X é o espaço total de um G -brado localmente trivial demos condições cação equivariante um grupo de Lie compacto e necessárias e sucientes para o correspondente problema de realização para aplicações G -equivariantes que preservam bra, onde G é um grupo nito.
Title in English
Realization of xed point set in a prescribed equivariant homotopy class of maps.
Keywords in English
Algebraic topology
Abstract in English
In this work, we combine the Nielsen fixed point theory with the transformation group theory to present necessary and sucient conditions for the realization of a locally contrac- G -subset A of X as the xed point set of a map h : X X in a given G -homotopy class. Here, G is a compact Lie group and X is a compact smooth G -manifold. In adition, if X is the total space of a G -ber bundle we present necessary and sucient conditions for the corresponding realization problem for G -ber-preserving maps when G tible is a nite group.
 
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Publishing Date
2019-06-04
 
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