Asymptotic property C of the wreath product ZwrZ
Jingming Zhu, Yan Wu
TL;DR
This paper demonstrates that the wreath product Z wr Z possesses asymptotic property C by analyzing its transfinite asymptotic dimension, which is shown to be at most omega+1.
Contribution
It establishes the asymptotic property C for Z wr Z through the relationship with transfinite asymptotic dimension, providing new insights into its large-scale geometric structure.
Findings
Z wr Z has asymptotic property C.
Transfinite asymptotic dimension of Z wr Z is at most omega+1.
Connects transfinite asymptotic dimension with asymptotic property C.
Abstract
Using the relationship between transfinite asymptotic dimension and asymptotic property C, we obtain that the wreath product Z wr Z has asymptotic property C. Specifically, we prove that the transfinite asymptotic dimension of the wreath product Z wr Z is no more than omega+ 1.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Holomorphic and Operator Theory · Geometric and Algebraic Topology