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. https://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 | |||||||||
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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. | |||||||||
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| Subject Keywords: | Countable Borel equivalence relations, structurability, simplicial complexes | |||||||||
| Issue or Number: | 7 | |||||||||
| Classification Code: | MSC (2010): Primary 03E15; Secondary 05E45 | |||||||||
| DOI: | 10.1090/proc/13957 | |||||||||
| Record Number: | CaltechAUTHORS:20180502-131620679 | |||||||||
| Persistent URL: | https://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: | 15 Nov 2021 20:36 |
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