Notes on treeability and costs for discrete groupoids in operator algebra framework

Details Notes on treeability and costs for discrete groupoids in operator algebra framework Notes on treeability and costs for discrete groupoids in operator algebra framework

2005-04-13

arxiv.org/abs/math/0504262v4

Mathematics

Operator Algebras

These notes are partly from the lectures we gave at University of Tokyo in Fall, 2004. Minor typos are corrected (June/4/05)

Scientific paper

We provide an operator algebraic interpretation of discrete measurable groupoids in the course of re-proving (and slightly generalizing) a result on treeability due to Adams and Spatzier. Then, we reconstruct Gaboriau's beautiful work on costs of equivalence relations in operator algebra framework, avoiding any measure theoretic argument, and clarify what kind of his results can or cannot be generalized to the non-principal groupoid case.

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