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arXiv:1605.01192 [math.GR]AbstractReferencesReviewsResources

Admitting a coarse embedding is not preserved under group extensions

Goulnara Arzhantseva, Romain Tessera

Published 2016-05-04Version 1

We construct a finitely generated group which is an extension of two groups coarsely embeddable into Hilbert space but which itself does not coarsely embed into Hilbert space. Our construction also provides a new infinite monster group: the first example of a finitely generated group that does not coarsely embed into Hilbert space and yet does not contain a weakly embedded expander.

Comments: 15 pages
Categories: math.GR, math.FA, math.MG
Subjects: 46B85, 20F69, 22D10, 20E22
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