In their study of almost group representations, Manuilov and Mishchenko introduced and investigated the notion of asymptotic stability of a finitely presented discrete group. In this paper we establish connections between connectivity of amenable groups and asymptotic stability and exhibit new classes of asymptotically stable groups. In particular, we show that if G is an amenable and connective discrete group whose classifying space BG is homotopic to a finite simplicial complex, then G is asymptotically stable.
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Connective Bieberbach groups
We prove that a Bieberbach group with trivial center is not connective and use this property to show that a Bieberbach group is connective if and only if it is poly-[Formula: see text].
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- Award ID(s):
- 1700086
- PAR ID:
- 10178917
- Date Published:
- Journal Name:
- International Journal of Mathematics
- Volume:
- 31
- Issue:
- 06
- ISSN:
- 0129-167X
- Page Range / eLocation ID:
- 2050047
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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