Some questions about the dimension of a group action

Details Some questions about the dimension of a group action Some questions about the dimension of a group action

2006-11-14

arxiv.org/abs/math/0611434v1

Mathematics

Group Theory

8 Pages, follows up on some loose ideas in "A geometric classification of some solvable groups of homeomorphisms." Arxiv: ma

Scientific paper

We discuss three families of groups, $ZW_n$, $PL(I^n)$, and $PL(S^n)$ (the last two being families of groups of piecewise-linear homeomorphisms of standard $n$-dimensional spaces). We note that for all positive integers $n$, $ZW_n$ embeds in $PL(I^n)$ which embeds in $PL(S^n)$. In another direction, $ZW_2$ fails to embed in $PL(I^1)$ by an earlier result of the author, and we extend that result to show that $ZW_2$ also fails to embed in $PL(S^1)$. The nature of the proofs of these non-embedding results leads us to ask if there are corresponding non-embedding results in higher dimensions.

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