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Borel structurability by locally finite simplicial complexes


Author: Ruiyuan Chen
Journal: Proc. Amer. Math. Soc. 146 (2018), 3085-3096
MSC (2010): Primary 03E15; Secondary 05E45
DOI: https://doi.org/10.1090/proc/13957
Published electronically: February 16, 2018
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Abstract: We show that every countable Borel equivalence relation structurable by $ n$-dimensional contractible simplicial complexes embeds into one which is structurable by such complexes with the further property that each vertex belongs to at most $ M_n := 2^{n-1}(n^2+3n+2)-2$ edges; this generalizes a result of Jackson-Kechris-Louveau in the case $ n = 1$. The proof is based on that of a classical result of Whitehead on countable CW-complexes.


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Additional Information

Ruiyuan Chen
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Email: rchen2@caltech.edu

DOI: https://doi.org/10.1090/proc/13957
Keywords: Countable Borel equivalence relations, structurability, simplicial complexes.
Received by editor(s): March 17, 2017
Received by editor(s) in revised form: September 13, 2017
Published electronically: February 16, 2018
Additional Notes: This research was partially supported by NSERC PGS D
Communicated by: Heike Mildenberger
Article copyright: © Copyright 2018 American Mathematical Society

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