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Limits of (certain) CAT(0) groups, I: Compactification

Daniel Groves

Algebraic & Geometric Topology 5 (2005) 1325–1364
Bibliography
1 M Bestvina, Degenerations of the hyperbolic space, Duke Math. J. 56 (1988) 143 MR932860
2 M Bestvina, $\mathbb R$–trees in topology, geometry, and group theory, from: "Handbook of geometric topology", North-Holland (2002) 55 MR1886668
3 M Bestvina, Questions in geometric group theory (2004)
4 M Bestvina, M Feighn, Stable actions of groups on real trees, Invent. Math. 121 (1995) 287 MR1346208
5 M Bestvina, M Feighn, Notes on Sela's work: Limit groups and Makanin–Razborov diagrams, preprint
6 L Bieberbach, Über die Bewegungsgruppen der Euklidischen Räume, Math. Ann. 70 (1911) 297 MR1511623
7 L Bieberbach, Über die Bewegungsgruppen der Euklidischen Räume (Zweite Abhandlung.) Die Gruppen mit einem endlichen Fundamentalbereich, Math. Ann. 72 (1912) 400 MR1511704
8 M R Bridson, A Haefliger, Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer (1999) MR1744486
9 M R Bridson, G A Swarup, On Hausdorff–Gromov convergence and a theorem of Paulin, Enseign. Math. $(2)$ 40 (1994) 267 MR1309129
10 C Champetier, L'espace des groupes de type fini, Topology 39 (2000) 657 MR1760424
11 C Champetier, V Guirardel, Limit groups as limits of free groups, Israel J. Math. 146 (2005) 1 MR2151593
12 I Chiswell, Introduction to $\Lambda$–trees, World Scientific Publishing Co. (2001) MR1851337
13 L van den Dries, A J Wilkie, Gromov's theorem on groups of polynomial growth and elementary logic, J. Algebra 89 (1984) 349 MR751150
14 C Druţu, M Sapir, Tree-graded spaces and asymptotic cones of groups, Topology 44 (2005) 959 MR2153979
15 D B A Epstein, J W Cannon, D F Holt, S V F Levy, M S Paterson, W P Thurston, Word processing in groups, Jones and Bartlett Publishers (1992) MR1161694
16 R I Grigorchuk, Degrees of growth of finitely generated groups and the theory of invariant means, Izv. Akad. Nauk SSSR Ser. Mat. 48 (1984) 939 MR764305
17 D Groves, Limit groups for (certain) CAT(0) groups II: The Hopf property and the shortening argument arXiv:math.GR/0408080
18 G C Hruska, Nonpositively curved spaces with isolated flats, PhD thesis, Cornell University (2002)
19 G C Hruska, B Kleiner, Hadamard spaces with isolated flats, Geom. Topol. 9 (2005) 1501 MR2175151
20 M Kapovich, B Leeb, On asymptotic cones and quasi-isometry classes of fundamental groups of 3–manifolds, Geom. Funct. Anal. 5 (1995) 582 MR1339818
21 O Kharlampovich, A Myasnikov, Elementary theory of free non-abelian groups, J. Algebra 302 (2006) 451 MR2293770
22 J W Morgan, P B Shalen, Valuations, trees, and degenerations of hyperbolic structures. I, Ann. of Math. $(2)$ 120 (1984) 401 MR769158
23 F Paulin, Topologie de Gromov équivariante, structures hyperboliques et arbres réels, Invent. Math. 94 (1988) 53 MR958589
24 F Paulin, Outer automorphisms of hyperbolic groups and small actions on $\mathbb{R}$–trees, from: "Arboreal group theory (Berkeley, CA, 1988)", Math. Sci. Res. Inst. Publ. 19, Springer (1991) 331 MR1105339
25 F Paulin, Sur la théorie élémentaire des groupes libres (d'après Sela), Astérisque (2004) 363 MR2111650
26 E Rips, Z Sela, Structure and rigidity in hyperbolic groups I, Geom. Funct. Anal. 4 (1994) 337 MR1274119
27 E Rips, Z Sela, Cyclic splittings of finitely presented groups and the canonical JSJ decomposition, Ann. of Math. $(2)$ 146 (1997) 53 MR1469317
28 Z Sela, The isomorphism problem for hyperbolic groups I, Ann. of Math. $(2)$ 141 (1995) 217 MR1324134
29 Z Sela, Structure and rigidity in (Gromov) hyperbolic groups and discrete groups in rank 1 Lie groups II, Geom. Funct. Anal. 7 (1997) 561 MR1466338
30 Z Sela, Acylindrical accessibility for groups, Invent. Math. 129 (1997) 527 MR1465334
31 Z Sela, Endomorphisms of hyperbolic groups I: The Hopf property, Topology 38 (1999) 301 MR1660337
32 Z Sela, Diophantine geometry over groups I: Makanin–Razborov diagrams, Publ. Math. Inst. Hautes Études Sci. (2001) 31 MR1863735
33 Z Sela, Diophantine geometry over groups VI: The elementary theory of a free group, preprint
34 Z Sela, Diophantine geometry over groups VII: The elementary theory of a hyperbolic group, preprint
35 Z Sela, Diophantine geometry over groups: a list of research problems
36 P B Shalen, Dendrology of groups: an introduction, from: "Essays in group theory", Math. Sci. Res. Inst. Publ. 8, Springer (1987) 265 MR919830
37 P B Shalen, Dendrology and its applications, from: "Group theory from a geometrical viewpoint (Trieste, 1990)", World Sci. Publ., River Edge, NJ (1991) 543 MR1170376
38 W P Thurston, Three-dimensional geometry and topology Vol. 1, Princeton Mathematical Series 35, Princeton University Press (1997) MR1435975
39 D T Wise, A non–Hopfian automatic group, J. Algebra 180 (1996) 845 MR1379212
40 D T Wise, Subgroup separability of the figure 8 knot group, Topology 45 (2006) 421 MR2218750