New York Journal of Mathematics
Volume 21 (2015) 129-150


Tullia Dymarz, Irine Peng, and Jennifer Taback

Bilipschitz versus quasi-isometric equivalence for higher rank lamplighter groups

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Published: February 23, 2015
Keywords: quasi-isometric equivalence, bilipschitz equivalence, higher rank lamplighter groups, Diestel-Leader graphs, Diestel-Leader groups
Subject: 20F65; 05C25, 05C63, 20E22

We describe a family of finitely presented groups which are quasi-isometric but not bilipschitz equivalent. The first such examples were described by the first author (Duke Math. J., 2010) and are the lamplighter groups F \wr Z where F is a finite group; these groups are finitely generated but not finitely presented. The examples presented in this paper are higher rank generalizations of these lamplighter groups and include groups that are of type Fn for any n.


The first author acknowledges support from National Science Foundation grant DMS-1207296. The third author acknowledges support from National Science Foundation grant DMS-1105407.

Author information

Tullia Dymarz:
Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, WI 53706

Irine Peng:
Department of Mathematics, Pohang University of Science and Technology, 31 San, Hyoja-dong, Namgu, Pohang, Gyeongsanbukdo, South Korea.

Jennifer Taback:
Department of Mathematics, Bowdoin College, 8600 College Station, Brunswick, ME 04011