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Triangle Joins of SP1 Equivalence Relations and their Cost

Teodor Stefan Bildea
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Abstract

Free joins of measure preserving equivalence relations, with or without amalgamation were introduced by Gaboriau, who studied their cost and obtained a formula for the cost of free products of groups. We introduce the notion of triangle join of measure preserving equivalence relations and study their cost. As a consequence we show that the cost of Thompson's group G is 1.

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Teodor Stefan Bildea. 2005-03-17. Triangle Joins of SP1 Equivalence Relations and their Cost. https://arxiv.org/abs/math/0503280

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