Proceedings of the American Mathematical Society

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
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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.

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)

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 20E06, 20F65, 20F36

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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ISSN 1088-6826 (e) ISSN 0002-9939 (p)

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