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Free <Emphasis Type="Italic">G</Emphasis>-spaces and maximal equivariant compactifications

Authors:	Email author" target="_blank">Natella?Antonyan Email author Email author" target="_blank">Sergey?Antonyan Email author

Institution:	(1) Departamento de Matemáticas, Division de Ingeniería y Arquitectura, Instituto Tecnológico y de Estudios Superiores de Monterrey, Campus Ciudad de México, 14380 México D.F., Mexico;(2) Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, 04510 México D.F., Mexico

Abstract:	For a compact Lie group G we prove that every free (resp., semifree) G-space admits a based-free (resp., semifree) G-compactification. Examples of finite- and infinite-dimensional G-spaces are presented that do not admit a free or based-free G-compactification. We give several characterizations of the maximal G-compactification β_GX that are further applied to prove the formula (β_GX)/H=β_G/H(X/H) for arbitrary closed normal subgroup H⊂G. Mathematics Subject Classification (2000) 54H15, 54D35

Keywords:	free G-space semifree G-space maximal G-compactification orbit space
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