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Borel structurability by locally finite simplicial complexes

Chen, Ruiyuan (2018) Borel structurability by locally finite simplicial complexes. Proceedings of the American Mathematical Society, 146 (7). pp. 3085-3096. ISSN 0002-9939. doi:10.1090/proc/13957.

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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:© 2018 American Mathematical Society. Received by the editors March 17, 2017, and, in revised form, September 13, 2017. Article electronically published on February 16, 2018. This research was partially supported by NSERC PGS D. The author would like to thank Alexander Kechris, Damien Gaboriau, and the anonymous referee for providing some comments on drafts of this paper.
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Subject Keywords:Countable Borel equivalence relations, structurability, simplicial complexes
Issue or Number:7
Classification Code:MSC (2010): Primary 03E15; Secondary 05E45
Record Number:CaltechAUTHORS:20180502-131620679
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86195
Deposited By: Tony Diaz
Deposited On:03 May 2018 21:11
Last Modified:15 Nov 2021 20:36

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