Admitting a coarse embedding is not preserved under group extensions
Group Theory
2017-10-04 v3 Functional Analysis
Metric Geometry
Abstract
We construct a finitely generated group which is an extension of two finitely generated 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.
Cite
@article{arxiv.1605.01192,
title = {Admitting a coarse embedding is not preserved under group extensions},
author = {Goulnara Arzhantseva and Romain Tessera},
journal= {arXiv preprint arXiv:1605.01192},
year = {2017}
}
Comments
15 pages; Proposition 3.3(v1) was modified following a comment of D. Sawicki; Theorem 2(v3) is new and gives an extension of finitely generated groups