The large scale geometry of some metabelian groups [article]

J. Taback, K. Whyte
2003 arXiv   pre-print
We study the large scale geometry of the upper triangular subgroup of PSL(2,Z[1/n]), which arises naturally in a geometric context. We prove a quasi-isometry classification theorem and show that these groups are quasi-isometrically rigid with infinite dimensional quasi-isometry group. We generalize our results to a larger class of groups which are metabelian and are higher dimensional analogues of the solvable Baumslag-Solitar groups BS(1,n).
arXiv:math/0301178v1 fatcat:ykauzo3ywbf4rebv3nwekvy65u