The Divergence of the Special Linear Group over a Function Ring

REFERENCES

• Behr , H. ( 1979 ). SL3(𝔽 q [t]) is not finitely presentable . In: Homological group theory. Proc. Sympos., Durham, 1977 . London Math. Soc. Lecture Note Ser. , Vol. 36 . Cambridge : Cambridge Univ. Press , pp. 213 – 224 .
   Google Scholar
• Brown , K. ( 1989 ). Buildings . New York : Springer-Verlag .
   Google Scholar
• Caprace , P. , Dahmani , F. , Guirardel , V. ( 2010 ). Twin building lattices do not have asymptotic cut-points . Geom. Dedicata 147 : 409 – 415 .
   Web of Science ®Google Scholar
• Cornulier , Y. ( 2008 ). Dimension of asymptotic cones of Lie groups . J. Topol. 1 ( 2 ): 342 – 361 .
   Web of Science ®Google Scholar
• Druţu , C. , Mozes , S. , Sapir , M. ( 2010 ). Divergence in lattices in semisimple Lie groups and graphs of groups . Trans. Amer. Math. Soc. 362 ( 5 ): 2451 – 2505 .
   Web of Science ®Google Scholar
• Druţu , C. , Sapir , M. ( 2005 ). Tree-graded spaces and asymptotic cones of groups . Topology , 44 ( 5 ): 959 – 1058 . with an appendix by D. Osin and M. Sapir .
   Web of Science ®Google Scholar
• Druţu , C. ( 2002 ). Quasi-isometry invariants and asymptotic cones . Internat. J. Algebra Comput. , 12 ( 1–2 ): 99 – 135 . International Conference on Geometric and Combinatorial Methods in Group Theory and Semigroup Theory (Lincoln, NE, 2000) .
   Web of Science ®Google Scholar
• Garrett , P. (1997). Buildings and Classical Groups . London : Chapman & Hall.
   Google Scholar
• Gromov , M. ( 1993 ). Asymptotic invariants of infinite groups . In: Geometric group theory, Vol. 2 (Sussex, 1991), volume 182 of London Math. Soc. Lecture Note Ser. , pages 1 – 295 . Cambridge : Cambridge Univ. Press .
   Google Scholar
• Kleiner , B. , Leeb , B. ( 1997 ). Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings . Inst. Hautes Études Sci. Publ. Math. 86 : 115 – 197 .
   Google Scholar
• Lubotzky , A. , Mozes , S. , Raghunathan , M. ( 1993 ). Cyclic subgroups of exponential growth and metrics on discrete groups . C. R. Acad. Sci. Paris Sér. I Math. 317 ( 8 ): 735 – 740 .
   Google Scholar
• Lubotzky , A. , Mozes , S. , Raghunathan , M. ( 2000 ). The word and Riemannian metrics on lattices of semisimple groups . Inst. Hautes Études Sci. Publ. Math. 91 : 5 – 53 .
   Google Scholar
• MacDuffee , C. ( 1956 ). The Theory of Matrices . New York : Chelsea Publishing Company .
   Google Scholar
• Nagao , H. ( 1959 ). On GL(2, K[x]) . J. Inst. Polytech. Osaka City Univ. Ser. A 10 : 117 – 121 .
   Google Scholar
• Stallings , J. R. ( 1968 ). On torsion-free groups with infinitely many ends . Ann. of Math. (2) 88 : 312 – 334 .
   Web of Science ®Google Scholar
• Weil , A. ( 1995 ). Basic Number Theory . Classics in Mathematics . Berlin : Springer-Verlag .
   Google Scholar
• Communicated by A. Olshanskii.
   Google Scholar