Article contents
COARSE COHERENCE OF METRIC SPACES AND GROUPS AND ITS PERMANENCE PROPERTIES
Published online by Cambridge University Press: 12 September 2018
Abstract
We introduce properties of metric spaces and, specifically, finitely generated groups with word metrics, which we call coarse coherence and coarse regular coherence. They are geometric counterparts of the classical algebraic notion of coherence and the regular coherence property of groups defined and studied by Waldhausen. The new properties can be defined in the general context of coarse metric geometry and are coarse invariants. In particular, they are quasi-isometry invariants of spaces and groups. The new framework allows us to prove structural results by developing permanence properties, including the particularly important fibering permanence property, for coarse regular coherence.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 98 , Issue 3 , December 2018 , pp. 422 - 433
- Copyright
- © 2018 Australian Mathematical Publishing Association Inc.
References
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20181116155047110-0481:S0004972718000977:S0004972718000977_inline1.gif?pub-status=live)
- 1
- Cited by