Published February 16, 2018
| Submitted
Journal Article
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Borel structurability by locally finite simplicial complexes
- Creators
- Chen, Ruiyuan
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.
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.Attached Files
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Additional details
- Eprint ID
- 86195
- Resolver ID
- CaltechAUTHORS:20180502-131620679
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- Created
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2018-05-03Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field