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Bulletin of the London Mathematical Society Advance Access originally published online on July 16, 2008
Bulletin of the London Mathematical Society 2008 40(5):770-776; doi:10.1112/blms/bdn060
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© 2008 London Mathematical Society

Some questions about the dimension of a group action

Collin Bleak

Department of Mathematics
University of Nebraska
Lincoln, NE 68588-0130
USA

Received 23 November 2006. Revision received 23 April 2008.

This article discusses three families of groups: Z {wreath} Zn, PL(In), and PL(Sn) (the last two being the families of groups of piecewise-linear homeomorphisms of standard n-dimensional spaces). It is shown that for positive n isin N, Z {wreath} Zn embeds in PL(In), which embeds in PL(Sn). It is known that Z {wreath} Z2 fails to embed in PL(I1), and this article extends that previous result to show that Z {wreath} Z2 also fails to embed in PL(S1). The nature of the proofs of these embedding and non-embedding results hints that there may be corresponding non-embedding results in higher dimensions.

2000 Mathematics Subject Classification 22S50, 37B05, 22F05, 37E10, 37E45.


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