Borel structurability by locally finite simplicial complexes
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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.References
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Additional Information
- Ruiyuan Chen
- Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
- MR Author ID: 1012788
- Email: rchen2@caltech.edu
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 3085-3096
- MSC (2010): Primary 03E15; Secondary 05E45
- DOI: https://doi.org/10.1090/proc/13957
- MathSciNet review: 3787369