Abstract
In this paper we prove quasi-isometric rigidity results concerning lattices in Sol and lamplighter groups. The paper builds in a substantial way on our earlier paper Coarse differentiation of quasi-isometries I: spaces not quasi-isometric to Cayley graphs.
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@book {dlH, MRKEY = {1786869},
AUTHOR = {de la Harpe, Pierre},
TITLE = {Topics in Geometric Group Theory},
SERIES = {Chicago Lectures in Mathematics},
PUBLISHER = {University of Chicago Press},
ADDRESS = {Chicago, IL},
YEAR = {2000},
PAGES = {vi+310},
ISBN = {0-226-31719-6; 0-226-31721-8},
MRCLASS = {20F65 (20F69 57M07)},
MRNUMBER = {1786869},
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ZBLNUMBER = {0965.20025},
} -
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@article {EFW0, MRKEY = {2402598},
AUTHOR = {Eskin, Alex and Fisher, David and Whyte, Kevin},
TITLE = {Quasi-isometries and rigidity of solvable groups},
JOURNAL = {Pure Appl. Math. Q.},
FJOURNAL = {Pure and Applied Mathematics Quarterly},
VOLUME = {3},
YEAR = {2007},
NUMBER = {4, part 1},
PAGES = {927--947},
ISSN = {1558-8599},
MRCLASS = {20F65 (22E25)},
MRNUMBER = {2402598},
MRREVIEWER = {Bachir Bekka},
ZBLNUMBER = {1167.22007},
} -
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@article {EFW1, MRKEY = {2925383},
AUTHOR = {Eskin, Alex and Fisher, David and Whyte, Kevin},
TITLE = {Coarse differentiation of quasi-isometries {I}: {S}paces not quasi-isometric to {C}ayley graphs},
JOURNAL = {Ann. of Math.},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {176},
YEAR = {2012},
NUMBER = {1},
PAGES = {221--260},
ISSN = {0003-486X},
CODEN = {ANMAAH},
MRCLASS = {22E25 (05C05 05C76 20F65)},
MRNUMBER = {2925383},
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@incollection {FM4, MRKEY = {1796128},
AUTHOR = {Farb, Benson and Mosher, Lee},
TITLE = {Problems on the geometry of finitely generated solvable groups},
BOOKTITLE = {Crystallographic Groups and their Generalizations},
VENUE={{K}ortrijk, 1999},
SERIES = {Contemp. Math.},
VOLUME = {262},
PAGES = {121--134},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {2000},
MRCLASS = {20F69 (20F16 22E25 57M07)},
MRNUMBER = {1796128},
MRREVIEWER = {Ilya Kapovich},
DOI = {10.1090/conm/262/04170},
ZBLNUMBER = {0983.20038},
} -
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@book {GhdlH, MRKEY = {1086648},
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VOLUME = {83},
NOTE = {papers from the Swiss Seminar on Hyperbolic Groups held in Bern, 1988},
EDITOR={Ghys, E. and de la Harpe, P.},
PUBLISHER = {Birkhäuser},
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PAGES = {xii+285},
ISBN = {0-8176-3508-4},
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[MN] R. Moeller, , 2001.
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YEAR = {2005},
NUMBER = {3},
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MRCLASS = {60C05 (05C25 60G50 60J45)},
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[W]
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@article {W, MRKEY = {2320169},
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ZBLNUMBER = {1137.20034},
}