Borel structurability by locally finite simplicial complexes

Chen, Ruiyuan

doi:10.1090/proc/13957

Borel structurability by locally finite simplicial complexes
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Proc. Amer. Math. Soc. 146 (2018), 3085-3096 Request permission

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.

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