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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. http://resolver.caltech.edu/CaltechAUTHORS:20180502-131620679

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1090/proc/13957DOIArticle
https://arxiv.org/abs/1702.07057arXivDiscussion Paper
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.
Funders:
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Subject Keywords:Countable Borel equivalence relations, structurability, simplicial complexes
Classification Code:MSC (2010): Primary 03E15; Secondary 05E45
Record Number:CaltechAUTHORS:20180502-131620679
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180502-131620679
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86195
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:03 May 2018 21:11
Last Modified:03 May 2018 21:11

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