Volume 1 (1998)

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

Martin R Bridson

Geometry & Topology Monographs 1 (1998) 99–116
DOI: 10.2140/gtm.1998.1.99
 arXiv: math.GR/9810188
Abstract
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If a class of finitely generated groups $\mathsc{G}$ is closed under isometric amalgamations along free subgroups, then every $G\in \mathsc{G}$ can be quasi-isometrically embedded in a group $\stackrel{̂}{G}\in \mathsc{G}$ 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
Publication
Received: 16 November 1997
Published: 21 October 1998
Authors
 Martin R Bridson Mathematical Institute 24–29 St Giles’ Oxford OX1 3LB