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Commensurability and QI classification of free products of finitely generated abelian groups
Author(s):
Jason
A.
Behrstock;
Tadeusz
Januszkiewicz;
Walter
D.
Neumann
Journal:
Proc. Amer. Math. Soc.
137
(2009),
811-813.
MSC (2000):
Primary 20E06, 20F65, 20F36
Posted:
September 4, 2008
MathSciNet review:
2457418
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Abstract:
We give the commensurability classifications of free products of finitely many finitely generated abelian groups. We show this coincides with the quasi-isometry classification and prove that this class of groups is quasi-isometrically rigid.
References:
-
- 1.
- H. Bass, The degree of polynomial growth of finitely generated nilpotent groups, Proc. London Math. Soc. 25 (1972), 603-614. MR 0379672 (52:577)
- 2.
- S. M. Gersten, Quasi-isometry invariance of cohomological dimension, Comptes Rendues Acad. Sci. Paris Série 1 Math. 316 (1993), 411-416. MR 1209258 (94b:20042)
- 3.
- M. Gromov, Groups of polynomial growth and expanding maps, IHES Sci. Publ. Math. 53 (1981), 53-73. MR 623534 (83b:53041)
- 4.
- P. Papasoglu and K. Whyte, Quasi-isometries between groups with infinitely many ends, Comment. Math. Helv. 77 (2002), no. 1, 133-144. MR 1898396 (2003c:20049)
- 5.
- K. Whyte, Amenability, bi-Lipschitz equivalence, and the von Neumann conjecture, Duke Math. J. 99 (1999), no. 1, 93-112. MR 1700742 (2001a:20064)
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Additional Information:
Jason
A.
Behrstock
Affiliation:
Department of Mathematics, Columbia University, New York, New York 10027
Email:
jason@math.columbia.edu
Tadeusz
Januszkiewicz
Affiliation:
Department of Mathematics, Ohio State University, Columbus, Ohio 43210 - and - Mathematical Institute of the Polish Academy of Sciences
Email:
tjan@math.ohio-state.edu
Walter
D.
Neumann
Affiliation:
Department of Mathematics, Barnard College, Columbia University, New York, New York 10027
Email:
neumann@math.columbia.edu
DOI:
10.1090/S0002-9939-08-09559-2
PII:
S 0002-9939(08)09559-2
Received by editor(s):
December 6, 2007,
Received by editor(s) in revised form:
February 13, 2008
Posted:
September 4, 2008
Additional Notes:
This research was supported under NSF grants no. DMS-0604524, DMS-0706259, and DMS-0456227
Communicated by:
Alexander N. Dranishnikov
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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