The fundamental group of a group acting on a topological space

Description: In 1966, F. Rhodes introduced the idea of the fundamental group of a group G of homeomorphisms of a topological space X. His article contains summarized proofs of important results and has been studied since then primarily because the category of transformation group is more general than the category of topological spaces. In this thesis, a thorough study for Rhodes's work is presented providing examples to enrich the theory. Dr. James Montaldi from University of Manchester has recently contributed to this theory with a more general and applicable way of Rhodes's main theorem. His results are also analyzed here.
En 1966, F. Rhodes introdujo la idea del grupo fundamental de un grupo G de homeomor smos de un espacio topol ogico X. Su art culo contiene demostraciones que resumen los resultados importantes y ha sido estudiado desde entonces, principalmente debido a que la categor a de grupo de transformacin es m as general que la categor a de los espacios topol ogicos. En esta tesis, un estudio a fondo del trabajo de Rhodes se presenta con ejemplos para enriquecer la teora. El Dr. James Montaldi de la Universidad de Manchester ha contribuido recientemente a esta teor a con una forma m as general y aplicable del teorema principal de Rhodes. Sus resultados tambi en se analizan aqu .