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Equi-variant and Stable Finite Decomposition Complexity

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Type
Preprint
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Submission Date
Identifiers
arXiv ID: 1509.08883
Source
arXiv
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Abstract

In this paper, we introduce and study various kinds of decomposition complexity. First, we give a characterization of residually finite groups having finite decomposition complexity (FDC). Secondly, we introduce equi-variant straight FDC (sFDC), and prove that a group having equi-variant sFDC if and only if its box space having sFDC. Finally, we show that elementary amenable groups have equi-variant sFDC by introducing something called stable FDC.

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