2012Groups Geometry and DynamicsOpen access

Universal Borel actions of countable groups

Simon Thomas

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Abstract

If the countable group G has a nonabelian free subgroup, then there exists a standard Borel G -space such that the corresponding orbit equivalence relation is countable universal. In this paper, we will consider the question of whether the converse also holds.

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If the countable group G has a nonabelian free subgroup, then there exists a standard Borel G -space such that the corresponding orbit equivalence relation is countable universal. In this paper, we will consider the question of whether the converse also holds.

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Available abstract

If the countable group G has a nonabelian free subgroup, then there exists a standard Borel G -space such that the corresponding orbit equivalence relation is countable universal. In this paper, we will consider the question of whether the converse also holds.

Key concepts: Mathematics, Countable set, Pure mathematics, Borel set, Second-countable space, Discrete mathematics

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