Kyoto Journal of Mathematics

Extending properties to relatively hyperbolic groups

Daniel A. Ramras and Bobby W. Ramsey

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Abstract

Consider a finitely generated group G that is relatively hyperbolic with respect to a family of subgroups H1,,Hn. We present an axiomatic approach to the problem of extending metric properties from the subgroups Hi to the full group G. We use this to show that both (weak) finite decomposition complexity and straight finite decomposition complexity are extendable properties. We also discuss the equivalence of two notions of straight finite decomposition complexity.

Article information

Source
Kyoto J. Math., Volume 59, Number 2 (2019), 343-356.

Dates
Received: 12 August 2016
Revised: 17 February 2017
Accepted: 22 February 2017
First available in Project Euclid: 18 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1547802013

Digital Object Identifier
doi:10.1215/21562261-2018-0017

Mathematical Reviews number (MathSciNet)
MR3960296

Zentralblatt MATH identifier
07080107

Subjects
Primary: 20F67: Hyperbolic groups and nonpositively curved groups
Secondary: 19D50: Computations of higher $K$-theory of rings [See also 13D15, 16E20] 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces 20F69: Asymptotic properties of groups

Keywords
relative hyperbolicity finite decomposition complexity asymptotic dimension Cayley graph

Citation

Ramras, Daniel A.; Ramsey, Bobby W. Extending properties to relatively hyperbolic groups. Kyoto J. Math. 59 (2019), no. 2, 343--356. doi:10.1215/21562261-2018-0017. https://projecteuclid.org/euclid.kjm/1547802013


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