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A study on the relationship between Gottlieb-Rhodes groups and Gottlieb-Fox groups

초록/요약 도움말

The purpose of this thesis is to study a condition how the nth Gottlieb- Rhodes group of a transformation group (X,G) is related to the nth Gottlieb- Fox group of its orbit space X/G. Firstly, we explain the notion of Gottlieb groups, Fox groups, Rhodes groups, Gottlieb-Fox groups and Gottlieb- Rhodes groups. Secondly, we survey some properties of preferred paths and preferred traces. Next, we study the result of Golasinski, Goncalves and Wong, which says, that if a group G acts freely and properly discontinuously on a based space (X,x_0), then the nth Rhodes group of (X,G) is isomorphic to the nth Fox group of its orbit space. Finally, we prove that under certain conditions on a based G- space (X,x_0), the nth Gottlieb-Rhodes group of (X,x_0,G) is isomorphic to the nth Gottlieb-Fox group of X/G.

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