Controlled embeddings into groups that have no nontrivial finite quotients
Abstract
If a class of finitely generated groups Curly(G) is closed under isometric amalgamations along free subgroups, then every G in Curly(G) can be quasiisometrically embedded in a group Hat(G) in Curly(G) that has no proper subgroups of finite index. Every compact, connected, nonpositively curved space X admits an isometric embedding into a compact, connected, nonpositively curved space Overline(X) such that Overline(X) has no nontrivial finitesheeted coverings.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 1998
 DOI:
 10.48550/arXiv.math/9810188
 arXiv:
 arXiv:math/9810188
 Bibcode:
 1998math.....10188B
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Geometric Topology;
 20E26;
 20E06;
 53C70;
 20F32;
 20F06
 EPrint:
 18 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon1/paper4.abs.html