Volume 14, issue 3 (2014)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24, 1 issue

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Algebraic ranks of $\mathrm{CAT}(0)$ groups

Raeyong Kim

Algebraic & Geometric Topology 14 (2014) 1627–1648
Bibliography
1 W Ballmann, Nonpositively curved manifolds of higher rank, Ann. of Math. 122 (1985) 597 MR819559
2 W Ballmann, P Eberlein, Fundamental groups of manifolds of nonpositive curvature, J. Differential Geom. 25 (1987) 1 MR873453
3 B H Bowditch, Relatively hyperbolic groups, Internat. J. Algebra Comput. 22 (2012) 1250016, 66 MR2922380
4 K Burns, R Spatzier, Manifolds of nonpositive curvature and their buildings, Inst. Hautes Études Sci. Publ. Math. (1987) 35 MR908215
5 P E Caprace, K Fujiwara, Rank-one isometries of buildings and quasi-morphisms of Kac–Moody groups, Geom. Funct. Anal. 19 (2010) 1296 MR2585575
6 D Cooper, D D Long, A W Reid, Infinite Coxeter groups are virtually indicable, Proc. Edinburgh Math. Soc. 41 (1998) 303 MR1626421
7 M W Davis, Groups generated by reflections and aspherical manifolds not covered by Euclidean space, Ann. of Math. 117 (1983) 293 MR690848
8 M W Davis, The geometry and topology of Coxeter groups, London Math. Soc. Monographs Series 32, Princeton Univ. Press (2008) MR2360474
9 M W Davis, T Januszkiewicz, Right-angled Artin groups are commensurable with right-angled Coxeter groups, J. Pure Appl. Algebra 153 (2000) 229 MR1783167
10 C Druţu, Relatively hyperbolic groups: Geometry and quasi-isometric invariance, Comment. Math. Helv. 84 (2009) 503 MR2507252
11 C Druţu, M Sapir, Tree-graded spaces and asymptotic cones of groups, Topology 44 (2005) 959 MR2153979
12 A Eskin, B Farb, Quasi-flats and rigidity in higher rank symmetric spaces, J. Amer. Math. Soc. 10 (1997) 653 MR1434399
13 B Farb, Relatively hyperbolic groups, Geom. Funct. Anal. 8 (1998) 810 MR1650094
14 C Gonciulea, Infinite Coxeter groups virtually surject onto $\mathbb{Z}$, Comment. Math. Helv. 72 (1997) 257 MR1470091
15 M Gromov, Hyperbolic groups, from: "Essays in group theory" (editor S M Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
16 P Hall, Finiteness conditions for soluble groups, Proc. London Math. Soc. 4 (1954) 419 MR0072873
17 G C Hruska, B Kleiner, Hadamard spaces with isolated flats, Geom. Topol. 9 (2005) 1501 MR2175151
18 M Kapovich, B Leeb, On asymptotic cones and quasi-isometry classes of fundamental groups of $3$–manifolds, Geom. Funct. Anal. 5 (1995) 582 MR1339818
19 B Kleiner, B Leeb, Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings, Inst. Hautes Études Sci. Publ. Math. (1997) 115 MR1608566
20 M Koubi, Croissance uniforme dans les groupes hyperboliques, Ann. Inst. Fourier (Grenoble) 48 (1998) 1441 MR1662255
21 D Krammer, The conjugacy problem for Coxeter groups, PhD thesis, Universiteit Utrecht (1994)
22 I Mineyev, A Yaman, Relative hyperbolicity and bounded cohomology (2006)
23 G Moussong, Hyperbolic Coxeter groups, PhD thesis, The Ohio State University (1988)
24 D V Osin, Relatively hyperbolic groups: Intrinsic geometry, algebraic properties, and algorithmic problems, Mem. Amer. Math. Soc. 843, Amer. Math. Soc (2006) MR2182268
25 A Ould Houcine, Embeddings in finitely presented groups which preserve the center, J. Algebra 307 (2007) 1 MR2278040
26 G Prasad, M S Raghunathan, Cartan subgroups and lattices in semi-simple groups, Ann. of Math. 96 (1972) 296 MR0302822
27 S Singh, Coxeter groups are not higher rank arithmetic groups arXiv:1208.6569
28 P Tukia, Convergence groups and Gromov's metric hyperbolic spaces, New Zealand J. Math. 23 (1994) 157 MR1313451
29 X Xie, Growth of relatively hyperbolic groups, Proc. Amer. Math. Soc. 135 (2007) 695 MR2262865
30 A Yaman, A topological characterisation of relatively hyperbolic groups, J. Reine Angew. Math. 566 (2004) 41 MR2039323