Geometry & Topology Monographs 1 (1998), The Epstein Birthday Schrift, paper no. 4, pages 99-116.

Controlled embeddings into groups that have no non-trivial finite quotients

Martin R Bridson

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 quasi-isometrically embedded in a group Hat(G) in Curly(G) that has no proper subgroups of finite index.
Every compact, connected, non-positively curved space X admits an isometric embedding into a compact, connected, non-positively curved space Overline(X) such that Overline(X) has no non-trivial finite-sheeted coverings.

Keywords. Finite quotients, embeddings, non-positive curvature

AMS subject classification. Primary: 20E26, 20E06, 53C70. Secondary: 20F32, 20F06.

E-print: arXiv:math.GR/9810188

Submitted: 16 November 1997. Published: 25 October 1998.

Notes on file formats

Martin R Bridson
Mathematical Institute, 24--29 St Giles', Oxford, OX1 3LB
Email: bridson@maths.ox.ac.uk

GT home page

EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 21 Apr 2006. For the current production of this journal, please refer to http://msp.warwick.ac.uk/.