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Sofic dimension for discrete measured groupoids


Authors: Ken Dykema, David Kerr and Mikaël Pichot
Journal: Trans. Amer. Math. Soc. 366 (2014), 707-748
MSC (2010): Primary 20L05, 20E06, 37A15
Published electronically: September 4, 2013
MathSciNet review: 3130315
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Abstract: For discrete measured groupoids preserving a probability measure we introduce a notion of sofic dimension that measures the asymptotic growth of the number of sofic approximations on larger and larger finite sets. In the case of groups we give a formula for free products with amalgamation over an amenable subgroup. We also prove a free product formula for measure-preserving actions.


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Additional Information

Ken Dykema
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
Email: kdykema@math.tamu.edu

David Kerr
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
Email: kerr@math.tamu.edu

Mikaël Pichot
Affiliation: Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada H3A 2K6
Email: mikael.pichot@mcgill.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05987-9
Received by editor(s): March 28, 2012
Published electronically: September 4, 2013
Additional Notes: The first author was partially supported by NSF grant DMS-0901220
The second author was partially supported by NSF grant DMS-0900938
The third author was partially supported by JSPS
Article copyright: © Copyright 2013 American Mathematical Society