Realization of xed point set in a prescribed equivariant homotopy class of maps.

Author(s)

Rafael Moreira de Souza

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI)
• Defense date: 2014-05-29

Examining board members

Peter Ngai Sing Wong; Daciberg Lima Goncalves; Thais Fernanda Mendes Monis; Weslem Liberato Silva; Daniel Vendruscolo

• Advisor: Peter Ngai Sing Wong; Lucilia Daruiz Borsari

Abstract

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. (AU)