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Hyperbolicity and cubulability are preserved under elementary equivalence

Simon André

Geometry & Topology 24 (2020) 1075–1147
Bibliography
1 I Agol, The virtual Haken conjecture, Doc. Math. 18 (2013) 1045 MR3104553
2 B Baumslag, Residually free groups, Proc. London Math. Soc. 17 (1967) 402 MR0215903
3 G Baumslag, On generalised free products, Math. Z. 78 (1962) 423 MR140562
4 M Bestvina, M Feighn, A combination theorem for negatively curved groups, J. Differential Geom. 35 (1992) 85 MR1152226
5 B H Bowditch, Cut points and canonical splittings of hyperbolic groups, Acta Math. 180 (1998) 145 MR1638764
6 T Delzant, L’image d’un groupe dans un groupe hyperbolique, Comment. Math. Helv. 70 (1995) 267 MR1324630
7 V Guirardel, G Levitt, JSJ decompositions of groups, 395 (2017) MR3758992
8 F Haglund, Finite index subgroups of graph products, Geom. Dedicata 135 (2008) 167 MR2413337
9 O Kharlampovich, A Myasnikov, Irreducible affine varieties over a free group, I : Irreducibility of quadratic equations and Nullstellensatz, J. Algebra 200 (1998) 472 MR1610660
10 O Kharlampovich, A Myasnikov, Elementary theory of free non-abelian groups, J. Algebra 302 (2006) 451 MR2293770
11 P A Linnell, On accessibility of groups, J. Pure Appl. Algebra 30 (1983) 39 MR716233
12 D Marker, Model theory: an introduction, 217, Springer (2002) MR1924282
13 J P McCammond, D T Wise, Coherence, local quasiconvexity, and the perimeter of 2–complexes, Geom. Funct. Anal. 15 (2005) 859 MR2221153
14 J P McCammond, D T Wise, Locally quasiconvex small-cancellation groups, Trans. Amer. Math. Soc. 360 (2008) 237 MR2342002
15 C Moioli, Graphes de groupes et groupes co-hopfiens, PhD thesis, Université Paul Sabatier – Toulouse III (2013)
16 J W Morgan, P B Shalen, Valuations, trees, and degenerations of hyperbolic structures, I, Ann. of Math. 120 (1984) 401 MR769158
17 A Y Ol’shanskiĭ, On residualing homomorphisms and G–subgroups of hyperbolic groups, Internat. J. Algebra Comput. 3 (1993) 365 MR1250244
18 A Ould Houcine, Limit groups of equationally Noetherian groups, from: "Geometric group theory" (editors G N Arzhantseva, L Bartholdi, J Burillo, E Ventura), Birkhäuser (2007) 103 MR2395792
19 C Perin, Elementary embeddings in torsion-free hyperbolic groups, Ann. Sci. Éc. Norm. Supér. 44 (2011) 631 MR2919979
20 C Reinfeldt, R Weidmann, Makanin–Razborov diagrams for hyperbolic groups, preprint (2014)
21 V N Remeslennikov, –free groups, Sibirsk. Mat. Zh. 30 (1989) 193 MR1043446
22 M Sageev, CAT(0) cube complexes and groups, from: "Geometric group theory" (editors M Bestvina, M Sageev, K Vogtmann), IAS/Park City Math. Ser. 21, Amer. Math. Soc. (2014) 7 MR3329724
23 P Scott, T Wall, Topological methods in group theory, from: "Homological group theory" (editor C T C Wall), London Math. Soc. Lecture Note Ser. 36, Cambridge Univ. Press (1979) 137 MR564422
24 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
25 Z Sela, Diophantine geometry over groups, I : Makanin–Razborov diagrams, Publ. Math. Inst. Hautes Études Sci. 93 (2001) 31 MR1863735
26 Z Sela, Diophantine geometry over groups, VI : The elementary theory of a free group, Geom. Funct. Anal. 16 (2006) 707 MR2238945
27 Z Sela, Diophantine geometry over groups, VII : The elementary theory of a hyperbolic group, Proc. Lond. Math. Soc. 99 (2009) 217 MR2520356
28 M Sykiotis, On subgroups of finite complexity in groups acting on trees, J. Pure Appl. Algebra 200 (2005) 1 MR2142347
29 W Szmielew, Elementary properties of Abelian groups, Fund. Math. 41 (1955) 203 MR72131
30 D T Wise, The structure of groups with a quasiconvex hierarchy, preprint (2012)