Large Scale Geometry of Nilpotent-By-Cyclic Groups
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- Title
- Large Scale Geometry of Nilpotent-By-Cyclic Groups
- Authors
- Peng, I
- Date Issued
- 2011-08
- Publisher
- Springer
- Abstract
- We show quasi-isometric rigidity for a class of finitely generated, non-polycyclic nilpotent-by-cyclic groups. Specifically, let Gamma(1), Gamma(2) be ascending HNN extensions of finitely generated nilpotent groups N-1 and N-2, such that Gamma(1) is irreducible (see Definition 1.1). If Gamma(1) and Gamma(2) are quasi-isometric to each other then N-1 and N-2 are virtual lattices in a common simply connected nilpotent Lie group (N) over tilde. As a consequence, we show the class of irreducible ascending HNN extensions of finitely generated nilpotent groups is quasi-isometrically rigid.
- Keywords
- Quasi-isometry; nilpotent groups; rigidity
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/15672
- DOI
- 10.1007/S00039-011-0129-4
- ISSN
- 1016-443X
- Article Type
- Article
- Citation
- Geometric and Functional Analysis, vol. 21, no. 4, page. 951 - 1000, 2011-08
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