Universal G-spaces for proper actions of locally compact groups

作者：Antonyan Natella^*; Antonyan Sergey A; Varela Velasco Ruben D

来源：Topology and Its Applications, 2012, 159(4): 1159-1168.

DOI：10.1016/j.topol.2011.11.036

• Proper action
• Orbit type
• Slice
• Large subgroup
• Cone

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 tau every locally compact, non-compact, sigma-compact group G of weight w(G) %26lt;= tau can act properly on R-tau \ {0} such that R-tau \ {0} contains a G-homeomorphic copy of every Tychonoff proper G-space of weight %26lt;= tau. The metric cones Cone(G/H) with H subset of 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 subset of G does not exceed the weight of G.

• 出版日期2012-3-1