Universal G-spaces for proper actions of locally compact groups |
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Authors: | Natella Antonyan Sergey A Antonyan |
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Institution: | a Departamento de Matemáticas, Division de Ingeniería y Arquitectura, Instituto Tecnológico y de Estudios Superiores de Monterrey, Campus Ciudad de México, 14380 México Distrito Federal, Mexico b Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, 04510 México Distrito Federal, Mexico |
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Abstract: | We establish the existence of universal G-spaces for proper actions of locally compact groups on Tychonoff spaces. A typical result sounds as follows: for each infinite cardinal number τ every locally compact, non-compact, σ-compact group G of weight w(G)?τ, can act properly on Rτ?{0} such that Rτ?{0} contains a G-homeomorphic copy of every Tychonoff proper G-space of weight ?τ. The metric cones Cone(G/H) with H⊂G a compact subgroup such that G/H is a manifold, are the main building blocks in our approach. As a byproduct we prove that the cardinality of the set of all conjugacy classes of such subgroups H⊂G does not exceed the weight of G. |
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Keywords: | 22F05 54C25 54C55 54H15 |
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