Geometry & Topology Volume 21, issue 6 (2017)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Quasi-isometric classification of right-angled Artin groups, I: The finite out case

Jingyin Huang

Geometry & Topology 21 (2017) 3467–3537

DOI: 10.2140/gt.2017.21.3467

Bibliography

1	A Abrams, N Brady, P Dani, M Duchin, R Young, Pushing fillings in right-angled Artin groups, J. Lond. Math. Soc. 87 (2013) 663 MR3073670
2	I Agol, The virtual Haken conjecture, Doc. Math. 18 (2013) 1045 MR3104553
3	H Baik, S h Kim, T Koberda, Right-angled Artin subgroups of the C^∞ diffeomorphism group of the real line, preprint (2014) arXiv:1404.5559
4	J Behrstock, R Charney, Divergence and quasimorphisms of right-angled Artin groups, Math. Ann. 352 (2012) 339 MR2874959
5	J A Behrstock, T Januszkiewicz, W D Neumann, Quasi-isometric classification of some high dimensional right-angled Artin groups, Groups Geom. Dyn. 4 (2010) 681 MR2727658
6	J Behrstock, B Kleiner, Y Minsky, L Mosher, Geometry and rigidity of mapping class groups, Geom. Topol. 16 (2012) 781 MR2928983
7	J A Behrstock, W D Neumann, Quasi-isometric classification of graph manifold groups, Duke Math. J. 141 (2008) 217 MR2376814
8	M Bestvina, N Brady, Morse theory and finiteness properties of groups, Invent. Math. 129 (1997) 445 MR1465330
9	M Bestvina, B Kleiner, M Sageev, The asymptotic geometry of right-angled Artin groups, I, Geom. Topol. 12 (2008) 1653 MR2421136
10	M Bestvina, B Kleiner, M Sageev, Quasiflats in CAT(0) 2–complexes, Algebr. Geom. Topol. 16 (2016) 2663 MR3572343
11	N Brady, J Meier, Connectivity at infinity for right angled Artin groups, Trans. Amer. Math. Soc. 353 (2001) 117 MR1675166
12	N Brady, T Riley, H Short, The geometry of the word problem for finitely generated groups, Birkhäuser (2007) MR2281936
13	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
14	P E Caprace, N Monod, Isometry groups of non-positively curved spaces: structure theory, J. Topol. 2 (2009) 661 MR2574740
15	P E Caprace, M Sageev, Rank rigidity for CAT(0) cube complexes, Geom. Funct. Anal. 21 (2011) 851 MR2827012
16	R Charney, An introduction to right-angled Artin groups, Geom. Dedicata 125 (2007) 141 MR2322545
17	R Charney, M W Davis, Finite K(π,1)s for Artin groups, from: "Prospects in topology" (editor F Quinn), Ann. of Math. Stud. 138, Princeton Univ. Press (1995) 110 MR1368655
18	R Charney, M Farber, Random groups arising as graph products, Algebr. Geom. Topol. 12 (2012) 979 MR2928902
19	M T Clay, C J Leininger, J Mangahas, The geometry of right-angled Artin subgroups of mapping class groups, Groups Geom. Dyn. 6 (2012) 249 MR2914860
20	C B Croke, B Kleiner, Spaces with nonpositive curvature and their ideal boundaries, Topology 39 (2000) 549 MR1746908
21	M W Davis, Groups generated by reflections and aspherical manifolds not covered by Euclidean space, Ann. of Math. 117 (1983) 293 MR690848
22	M B Day, Finiteness of outer automorphism groups of random right-angled Artin groups, Algebr. Geom. Topol. 12 (2012) 1553 MR2966695
23	C Droms, Isomorphisms of graph groups, Proc. Amer. Math. Soc. 100 (1987) 407 MR891135
24	M J Dunwoody, The accessibility of finitely presented groups, Invent. Math. 81 (1985) 449 MR807066
25	A Eskin, Quasi-isometric rigidity of nonuniform lattices in higher rank symmetric spaces, J. Amer. Math. Soc. 11 (1998) 321 MR1475886
26	A Eskin, B Farb, Quasi-flats and rigidity in higher rank symmetric spaces, J. Amer. Math. Soc. 10 (1997) 653 MR1434399
27	B Farb, M Handel, Commensurations of Out(F_n), Publ. Math. Inst. Hautes Études Sci. 105 (2007) 1 MR2354204
28	V N Gerasimov, Semi-splittings of groups and actions on cubings, from: "Algebra, geometry, analysis and mathematical physics" (editors Y G Reshetnyak, L A Bokut’, S K Vodop’yanov, I A Taĭmanov), Izdat. Ross. Akad. Nauk Sib. Otd. Inst. Mat. (1997) 91 MR1624115
29	M Gromov, Hyperbolic groups, from: "Essays in group theory" (editor S M Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
30	M F Hagen, Weak hyperbolicity of cube complexes and quasi-arboreal groups, J. Topol. 7 (2014) 385 MR3217625
31	M F Hagen, D T Wise, Cubulating hyperbolic free-by-cyclic groups: the general case, Geom. Funct. Anal. 25 (2015) 134 MR3320891
32	M F Hagen, D T Wise, Cubulating hyperbolic free-by-cyclic groups: the irreducible case, Duke Math. J. 165 (2016) 1753 MR3513573
33	F Haglund, Isometries of CAT(0) cube complexes are semi-simple, preprint (2007) arXiv:0705.3386
34	F Haglund, Finite index subgroups of graph products, Geom. Dedicata 135 (2008) 167 MR2413337
35	F Haglund, D T Wise, Special cube complexes, Geom. Funct. Anal. 17 (2008) 1551 MR2377497
36	F Haglund, D T Wise, Coxeter groups are virtually special, Adv. Math. 224 (2010) 1890 MR2646113
37	U Hamenstädt, Geometry of the mapping class groups, III : Quasi-isometric rigidity, preprint (2005) arXiv:math/0512429
38	J Huang, Quasi-isometry classification of right-angled Artin groups, II: Several infinite out cases, preprint (2016) arXiv:1603.02372
39	J Huang, Top-dimensional quasiflats in CAT(0) cube complexes, Geom. Topol. 21 (2017) 2281 MR3654109
40	J Huang, B Kleiner, Groups quasi-isometric to RAAG’s, preprint (2016) arXiv:1601.00946
41	M Kapovich, B Kleiner, B Leeb, Quasi-isometries and the de Rham decomposition, Topology 37 (1998) 1193 MR1632904
42	S h Kim, T Koberda, Embedability between right-angled Artin groups, Geom. Topol. 17 (2013) 493 MR3039768
43	S H Kim, T Koberda, The geometry of the curve graph of a right-angled Artin group, Internat. J. Algebra Comput. 24 (2014) 121 MR3192368
44	S h Kim, T Koberda, Anti-trees and right-angled Artin subgroups of braid groups, Geom. Topol. 19 (2015) 3289 MR3447104
45	B Kleiner, B Leeb, Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings, C. R. Acad. Sci. Paris Sér. I Math. 324 (1997) 639 MR1447034
46	B Kleiner, B Leeb, Groups quasi-isometric to symmetric spaces, Comm. Anal. Geom. 9 (2001) 239 MR1846203
47	T Koberda, Ping-pong lemmas with applications to geometry and topology, from: "Geometry, topology and dynamics of character varieties" (editors W Goldman, C Series, S P Tan), Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. 23, World Scientific (2012) 139 MR2987617
48	T Koberda, Right-angled Artin groups and a generalized isomorphism problem for finitely generated subgroups of mapping class groups, Geom. Funct. Anal. 22 (2012) 1541 MR3000498
49	M R Laurence, A generating set for the automorphism group of a graph group, J. London Math. Soc. 52 (1995) 318 MR1356145
50	L Mosher, M Sageev, K Whyte, Quasi-actions on trees, II : Finite depth Bass–Serre trees, 1008, Amer. Math. Soc. (2011) MR2867450
51	G D Mostow, Strong rigidity of locally symmetric spaces, 78, Princeton Univ. Press (1973) MR0385004
52	Y Ollivier, D T Wise, Cubulating random groups at density less than 1∕6, Trans. Amer. Math. Soc. 363 (2011) 4701 MR2806688
53	P Papasoglu, K Whyte, Quasi-isometries between groups with infinitely many ends, Comment. Math. Helv. 77 (2002) 133 MR1898396
54	P Przytycki, D T Wise, Mixed 3-manifolds are virtually special, preprint (2012) arXiv:1205.6742
55	P Przytycki, D T Wise, Graph manifolds with boundary are virtually special, J. Topol. 7 (2014) 419 MR3217626
56	M Sageev, Ends of group pairs and non-positively curved cube complexes, Proc. London Math. Soc. 71 (1995) 585 MR1347406
57	H Servatius, Automorphisms of graph groups, J. Algebra 126 (1989) 34 MR1023285
58	H Servatius, C Droms, B Servatius, Surface subgroups of graph groups, Proc. Amer. Math. Soc. 106 (1989) 573 MR952322
59	S J Taylor, Right-angled Artin groups and Out(𝔽_n), I : Quasi-isometric embeddings, Groups Geom. Dyn. 9 (2015) 275 MR3343354
60	D T Wise, Cubulating small cancellation groups, Geom. Funct. Anal. 14 (2004) 150 MR2053602
61	D T Wise, Research announcement: the structure of groups with a quasiconvex hierarchy, Electron. Res. Announc. Math. Sci. 16 (2009) 44 MR2558631
62	D T Wise, The structure of groups with a quasiconvex hierarchy, preprint (2011)