Geometry & Topology Volume 11, issue 2 (2007)

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Quasi-isometric rigidity of higher rank $S$–arithmetic lattices

Kevin Wortman

Geometry & Topology 11 (2007) 995–1048

DOI: 10.2140/gt.2007.11.995

Bibliography

1	H Abels, Finiteness properties of certain arithmetic groups in the function field case, Israel J. Math. 76 (1991) 113 MR1177335
2	P Abramenko, Finiteness properties of Chevalley groups over $\mathbb{F}_q[t]$, Israel J. Math. 87 (1994) 203 MR1286827
3	H Behr, $\mathrm{SL}_3(\mathbb{F}_q[t])$ is not finitely presentable, from: "Homological group theory (Proc. Sympos., Durham, 1977)", London Math. Soc. Lecture Note Ser. 36, Cambridge Univ. Press (1979) 213 MR564424
4	F Blume, Ergodic theory, from: "Handbook of measure theory, Vol. II", North–Holland (2002) 1185 MR1954639
5	A Borel, Density and maximality of arithmetic subgroups, J. Reine Angew. Math. 224 (1966) 78 MR0205999
6	A Borel, Linear algebraic groups, Graduate Texts in Mathematics 126, Springer (1991) MR1102012
7	A Borel, T A Springer, Rationality properties of linear algebraic groups. II, Tôhoku Math. J. $(2)$ 20 (1968) 443 MR0244259
8	A Borel, J Tits, Homomorphismes “abstraits” de groupes algébriques simples, Ann. of Math. $(2)$ 97 (1973) 499 MR0316587
9	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften, Springer (1999) MR1744486
10	K S Brown, Buildings, Springer (1989) MR969123
11	C Druţu, Quasi-isometric classification of non-uniform lattices in semisimple groups of higher rank, Geom. Funct. Anal. 10 (2000) 327 MR1771426
12	A Eskin, Quasi-isometric rigidity of nonuniform lattices in higher rank symmetric spaces, J. Amer. Math. Soc. 11 (1998) 321 MR1475886
13	A Eskin, B Farb, Quasi-flats and rigidity in higher rank symmetric spaces, J. Amer. Math. Soc. 10 (1997) 653 MR1434399
14	B Farb, The quasi-isometry classification of lattices in semisimple Lie groups, Math. Res. Lett. 4 (1997) 705 MR1484701
15	B Farb, R Schwartz, The large-scale geometry of Hilbert modular groups, J. Differential Geom. 44 (1996) 435 MR1431001
16	G Harder, Über die Galoiskohomologie halbeinfacher algebraischer Gruppen III, J. Reine Angew. Math. 274/275 (1975) 125 MR0382469
17	B Kleiner, B Leeb, Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings, Inst. Hautes Études Sci. Publ. Math. 86 (1997) 115 MR1608566
18	A Lubotzky, S Mozes, M S Raghunathan, The word and Riemannian metrics on lattices of semisimple groups, Inst. Hautes Études Sci. Publ. Math. 91 (2000) 5 MR1828742
19	G A Margulis, Discrete subgroups of semisimple Lie groups, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), Springer (1991) MR1090825
20	G D Mostow, Strong rigidity of locally symmetric spaces, Annals of Mathematics Studies 78, Princeton University Press (1973) MR0385004
21	V Platonov, A Rapinchuk, Algebraic groups and number theory, Pure and Applied Mathematics 139, Academic Press (1994) MR1278263
22	G Prasad, Strong rigidity of $\mathbb{Q}$–rank $1$ lattices, Invent. Math. 21 (1973) 255 MR0385005
23	G Prasad, Strong approximation for semi-simple groups over function fields, Ann. of Math. $(2)$ 105 (1977) 553 MR0444571
24	G Prasad, Lattices in semisimple groups over local fields, from: "Studies in algebra and number theory", Adv. in Math. Suppl. Stud. 6, Academic Press (1979) 285 MR535769
25	M Ratner, On the $p$–adic and $S$–arithmetic generalizations of Raghunathan's conjectures, from: "Lie groups and ergodic theory (Mumbai, 1996)", Tata Inst. Fund. Res. Stud. Math. 14, Tata Inst. Fund. Res. (1998) 167 MR1699365
26	R E Schwartz, The quasi-isometry classification of rank one lattices, Inst. Hautes Études Sci. Publ. Math. 82 (1995) MR1383215
27	R E Schwartz, Quasi-isometric rigidity and Diophantine approximation, Acta Math. 177 (1996) 75 MR1417087
28	J Taback, Quasi-isometric rigidity for $\mathrm{PSL}_2(\mathbb{Z}[1/p])$, Duke Math. J. 101 (2000) 335 MR1738174
29	J Tits, Algebraic and abstract simple groups, Ann. of Math. $(2)$ 80 (1964) 313 MR0164968
30	J Tits, Buildings of spherical type and finite BN–pairs, Lecture Notes in Mathematics 386, Springer (1974) MR0470099
31	T N Venkataramana, On superrigidity and arithmeticity of lattices in semisimple groups over local fields of arbitrary characteristic, Invent. Math. 92 (1988) 255 MR936083
32	K Wortman, Quasiflats with holes in reductive groups, Algebr. Geom. Topol. 6 (2006) 91 MR2199455
33	K Wortman, Quasi-isometries of $\mathbf{SL}_n(\mathbb{F}_q[t])$, (in preparation)