TY - JOUR
T1 - Radius of comparison and mean cohomological independence dimension
AU - Hirshberg, Ilan
AU - Phillips, N. Christopher
N1 - Publisher Copyright:
© 2022 Elsevier Inc.
PY - 2022/9/17
Y1 - 2022/9/17
N2 - We introduce a notion of mean cohomological independence dimension for actions of discrete amenable groups on compact metrizable spaces, as a variant of mean dimension, and use it to obtain lower bounds for the radius of comparison of the associated crossed product C⁎-algebras. Our general theory, gives the following for the minimal subshifts constructed by Dou in 2017. For any countable amenable group G and any polyhedron Z, Dou's subshift T of ZG with density parameter ρ satisfies [Formula presented] If k=dim(Z) is even and Hˇk(Z;Q)≠0, then [Formula presented] regardless of what ρ is.
AB - We introduce a notion of mean cohomological independence dimension for actions of discrete amenable groups on compact metrizable spaces, as a variant of mean dimension, and use it to obtain lower bounds for the radius of comparison of the associated crossed product C⁎-algebras. Our general theory, gives the following for the minimal subshifts constructed by Dou in 2017. For any countable amenable group G and any polyhedron Z, Dou's subshift T of ZG with density parameter ρ satisfies [Formula presented] If k=dim(Z) is even and Hˇk(Z;Q)≠0, then [Formula presented] regardless of what ρ is.
KW - C-algebras
KW - Mean dimension
KW - Radius of comparison
UR - http://www.scopus.com/inward/record.url?scp=85134338402&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2022.108563
DO - 10.1016/j.aim.2022.108563
M3 - Article
AN - SCOPUS:85134338402
SN - 0001-8708
VL - 406
JO - Advances in Mathematics
JF - Advances in Mathematics
M1 - 108563
ER -