Residual finiteness growths of virtually special groups
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- 作者：Khalid Bou-Rabee (1)
Mark F. Hagen (2)
Priyam Patel (3)
1. Department of Mathematics ; The City College of New York ; NAC 8/133 ; Convent Ave at 138th Street ; New York ; NY ; 10031 ; USA
2. Department of Mathematics ; University of Michigan ; Ann Arbor ; MI ; USA
3. Department of Mathematics ; Purdue University ; West Lafayette ; IN ; USA - 关键词：Residual finiteness growth ; Special cube complex ; Right ; angled Artin group ; Primary 20E26 ; Secondary 20F65 ; 20F36
- 刊名：Mathematische Zeitschrift
- 出版年：2015
- 出版时间：February 2015
- 年：2015
- 卷：279
- 期：1-2
- 页码：297-310
- 全文大小：446 KB
- 参考文献：1. Aschenbrenner, M., Friedl, S., Wilton, H.: 3-manifold groups. arXiv:1205.0202, pp. 1鈥?49 (2013)
2. Agol, I.: The virtual Haken conjecture. arXiv:1204.2810, 2012. Primary article by Ian Agol, with an appendix by Ian Agol, Daniel Groves, and Jason Manning (2012)
3. Bigelow, S.J.: Braid groups are linear. J. Am. Math. Soc 14(2), 471鈥?86 (2001). (electronic) CrossRef
4. Bou-Rabee, K.: Quantifying residual finiteness. J. Algebra 323(3), 729鈥?37 (2010) CrossRef
5. Bou-Rabee, K.: Approximating a group by its solvable quotients. New York J. Math. 17, 699鈥?12 (2011)
6. Bridson, M.R.: Geodesics and curvature in metric simplicial complexes. In: Ghys, E., Haefliger, A., Verjovsky, A. (eds.) Group Theory from a Geometrical Viewpoint, Proceedings of the ICTP, Trieste, Italy, pp. 373鈥?63. World Scientific, Singapore (1991)
7. Bou-Rabee, K., Kaletha, T.: Quantifying residual finiteness of arithmetic groups. Compos. Math. 148(3), 907鈥?20 (2012) CrossRef
8. Bou-Rabee, K., McReynolds, D.B.: Extremal behaviour of divisibility functions. Geometriae Dedicata. (2014). doi:10.1007/s10711-014-9955-5
9. Bou-Rabee, K., McReynolds, D.B.: Bertrand鈥檚 postulate and subgroup growth. J. Algebra 324(4), 793鈥?19 (2010) CrossRef
10. Bou-Rabee, K., McReynolds, D.B.: Asymptotic growth and least common multiples in groups. Bull. Lond. Math. Soc. 43(6), 1059鈥?068 (2011) CrossRef
11. Buskin, N.V.: Efficient separability in free groups. Sibirsk. Mat. Zh. 50(4), 765鈥?71 (2009)
12. Charney, R., Davis, M.W.: Finite \(K(\pi ,1)\) s for Artin groups. In: Prospects in Topology (Princeton, NJ, 1994), volume 138 of Ann. of Math. Stud., pp. 110鈥?24. Princeton Univ. Press, Princeton (1995)
13. Charney, R.: An introduction to right-angled Artin groups. Geom. Dedic. 125, 141鈥?58 (2007) CrossRef
14. Chepoi, V.: Graphs of some \({\rm CAT}(0)\) complexes. Adv. Appl. Math. 24(2), 125鈥?79 (2000) CrossRef
15. Caprace, P.-E., Sageev, M.: Rank rigidity for CAT(0) cube complexes. Geom. Funct. Anal. 21, 851鈥?91 (2011) CrossRef
16. Cohen, A.M., Wales, D.B.: Linearity of Artin groups of finite type. Israel J. Math. 131, 101鈥?23 (2002) CrossRef
17. Gromov, M.: Hyperbolic groups. In: Essays in Group Theory, volume 8 of Math. Sci. Res. Inst. Publ., pp. 75鈥?63. Springer, New York (1987)
18. Grunewald, F.J., Segal, D., Smith, G.C.: Subgroups of finite index in nilpotent groups. Invent. Math. 93(1), 185鈥?23 (1988) CrossRef
19. Hagen, M.F.: Geometry and combinatorics of cube complexes. PhD thesis, McGill University (2012)
20. Haglund, F., Wise, D.T.: Special cube complexes. Geom. Funct. Anal. 17(5), 1551鈥?620 (2008) CrossRef
21. Haglund, F., Wise, D.T.: Coxeter groups are virtually special. Adv. Math. 224(5), 1890鈥?903 (2010) CrossRef
22. Haglund, F., Wise, D.T.: A combination theorem for special cube complexes. Ann. Math. (2) 176(3), 1427鈥?482 (2012) CrossRef
23. Hagen, M.F., Wise, D.T.: Cubulating hyperbolic free-by-cyclic groups: the irreducible case. arXiv:1311.2084, pp. 1鈥?9 (2013)
24. Kassabov, M., Biringer, I., Bou-Rabee, K., Matucci, F.: Intersection growth in groups (in preparation)
25. Kassabov, M., Matucci, F.: Bounding the residual finiteness of free groups. Proc. Am. Math. Soc. 139(7), 2281鈥?286 (2011) CrossRef
26. Krammer, D.: Braid groups are linear. Ann. Math. (2) 155(1), 131鈥?56 (2002) CrossRef
27. Leary, I.: A metric Kan-Thurston theorem. J. Topol. 6(1), 251鈥?84 (2013). doi:10.1112/jtopol/jts035
28. Liu, Y.: Virtual cubulation of nonpositively curved graph manifolds. J. Topol. 6(4), 793鈥?22 (2013). doi:10.1112/jtopol/jtt010
29. Lubotzky, A., Mozes, S., Raghunathan, M.S.: The word and Riemannian metrics on lattices of semisimple groups. Inst. Hautes 脡tudes Sci. Publ. Math. 91, 5鈥?3 (2001)
30. Niblo, G.A., Reeves, L.D.: Coxeter groups act on \({\rm CAT}(0)\) cube complexes. J. Group Theory 6(3), 399鈥?13 (2003) CrossRef
31. Ollivier, Y., Wise, D.T.: Cubulating random groups at density \(<\frac{1}{6}\) . Trans. Am. Math. Soc. 363, 4701鈥?733 (2011) CrossRef
32. Patel, P.: On a theorem of Peter Scott. Proceedings of the American Mathematical Society (2012, to appear)
33. Przytycki, P., Wise, D.T.: Mixed 3-manifolds are virtually special, pp. 1鈥?4. arXiv:1205.6742
34. Przytycki, P., Wise, D.T.: Graph manifolds with boundary are virtually special. arxiv:eprint.1110.3513, p. 24 (2011)
35. Riley, T.R.: Navigating in the Cayley graphs of \(\text{ SL }_N({\mathbb{Z}})\) and \(\text{ SL }_N({\mathbb{F}}_p)\) . Geom. Dedicata 113, 215鈥?29 (2005) CrossRef
36. Rivin, I.: Geodesics with one self-intersection, and other stories. Adv. Math. 231(5), 2391鈥?412 (2012) CrossRef
37. Sageev, M.: Ends of group pairs and non-positively curved cube complexes. Proc. Lond. Math. Soc. (3) 71(3), 585鈥?17 (1995) CrossRef
38. Stallings, J.R.: Topology of finite graphs. Inventiones Mathematicae 71(3), 551鈥?65 (1983) CrossRef
39. Wise, D.T.: The structure of groups with a quasiconvex hierarchy, 205 pp. (2011, preprint). www.math.mcgill.ca/~wise
40. Wise, D.T.: From riches to RAAGs: 3-manifolds, right-angled Artin groups, and cubical geometry. In: Lecture notes, NSF-CBMS Conference, CUNY Graduate Center, New York (2012) - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics - 出版者：Springer Berlin / Heidelberg
- ISSN：1432-1823
文摘
Let \(G\) be a virtually special group. Then the residual finiteness growth of \(G\) is at most linear. This result cannot be found by embedding \(G\) into a special linear group. Indeed, the special linear group \({{\mathrm{SL}}}_k(\mathbb {Z})\) , for \(k > 2\) , has residual finiteness growth \(n^{k-1}\) .