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 -