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COARSE COHERENCE OF METRIC SPACES AND GROUPS AND ITS PERMANENCE PROPERTIES

Part of: Homological methods Metric geometry Homological algebra

Published online by Cambridge University Press:  12 September 2018

BORIS GOLDFARB Open the ORCID record for BORIS GOLDFARB [Opens in a new window]  and
JONATHAN L. GROSSMAN Open the ORCID record for JONATHAN L. GROSSMAN [Opens in a new window]
BORIS GOLDFARB*
Affiliation:
Department of Mathematics and Statistics, SUNY, Albany, NY 12222, USA email bgoldfarb@albany.edu
JONATHAN L. GROSSMAN
Affiliation:
Department of Mathematics and Statistics, SUNY, Albany, NY 12222, USA email algrossman@albany.edu
*
✉bgoldfarb@albany.edu
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Abstract

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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.

Keywords

coherencecoarse coherenceregular coherenceweak regular coherencemetric spacepermanence

MSC classification

Primary: 16E65: Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
Secondary: 18G99: None of the above, but in this section 51F99: None of the above, but in this section
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. 

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