Geometry & Topology Volume 19, issue 2 (2015)

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Limit groups over partially commutative groups and group actions on real cubings

Montserrat Casals-Ruiz and Ilya Kazachkov

Geometry & Topology 19 (2015) 725–852

DOI: 10.2140/gt.2015.19.725

Bibliography

1	R C Alperin, K N Moss, Complete trees for groups with a real-valued length function, J. London Math. Soc. 31 (1985) 55 MR810562
2	A Baudisch, Kommutationsgleichungen in semifreien Gruppen, Acta Math. Acad. Sci. Hungar. 29 (1977) 235 MR0463300
3	G Baumslag, A Myasnikov, V N Remeslennikov, Algebraic geometry over groups, I: Algebraic sets and ideal theory, J. Algebra 219 (1999) 16 MR1707663
4	J Behrstock, R Charney, Divergence and quasimorphisms of right-angled Artin groups, Math. Ann. 352 (2012) 339 MR2874959
5	M Bestvina, N Brady, Morse theory and finiteness properties of groups, Invent. Math. 129 (1997) 445 MR1465330
6	R Bieri, Normal subgroups in duality groups and in groups of cohomological dimension $2$, J. Pure Appl. Algebra 7 (1976) 35 MR0390078
7	V Blatherwick, Centralisers and big powers in partially commutative groups, PhD thesis, University of Newcastle-upon-Tyne (2007)
8	B H Bowditch, Coarse median spaces and groups, Pacific J. Math. 261 (2013) 53 MR3037559
9	M R Bridson, A Haefliger, Metric spaces of nonpositive curvature, Grundl. Math. Wissen. 319, Springer (1999) MR1744486
10	M R Bridson, J Howie, C F Miller III, H Short, Finitely presented residually free groups, arXiv:0809.3704
11	M R Bridson, D H Kochloukova, Volume gradients and homology in towers of residually-free groups, arXiv:1309.1877
12	M Burger, S Mozes, Finitely presented simple groups and products of trees, C. R. Acad. Sci. Paris Sér. I Math. 324 (1997) 747 MR1446574
13	M Casals-Ruiz, I V Kazachkov, Elements of algebraic geometry and the positive theory of partially commutative groups, Canad. J. Math. 62 (2010) 481 MR2666386
14	M Casals-Ruiz, I V Kazachkov, On systems of equations over free partially commutative groups, Mem. Amer. Math. Soc. 212, Amer. Math. Soc. (2011) MR2817144
15	C Champetier, V Guirardel, Limit groups as limits of free groups, Israel J. Math. 146 (2005) 1 MR2151593
16	I M Chiswell, Abstract length functions in groups, Math. Proc. Cambridge Philos. Soc. 80 (1976) 451 MR0427480
17	L P Comerford Jr., C C Edmunds, Quadratic equations over free groups and free products, J. Algebra 68 (1981) 276 MR608536
18	J Crisp, B Wiest, Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups, Algebr. Geom. Topol. 4 (2004) 439 MR2077673
19	E Daniyarova, A Myasnikov, V N Remeslennikov, Unification theorems in algebraic geometry, from: "Aspects of infinite groups" (editors B Fine, G Rosenberger, D Spellman), Algebra Discrete Math. 1, World Scientific (2008) 80 MR2571513
20	V Diekert, A Muscholl, Solvability of equations in graph groups is decidable, Internat. J. Algebra Comput. 16 (2006) 1047 MR2286422
21	G Duchamp, D Krob, Partially commutative Magnus transformations, Internat. J. Algebra Comput. 3 (1993) 15 MR1214003
22	A J Duncan, I V Kazachkov, V N Remeslennikov, Parabolic and quasiparabolic subgroups of free partially commutative groups, J. Algebra 318 (2007) 918 MR2371978
23	A Dyubina, I Polterovich, Explicit constructions of universal $\mathbb R$–trees and asymptotic geometry of hyperbolic spaces, Bull. London Math. Soc. 33 (2001) 727 MR1853785
24	E S Esyp, I V Kazachkov, V N Remeslennikov, Divisibility theory and complexity of algorithms for free partially commutative groups, from: "Groups, languages, algorithms" (editor A V Borovik), Contemp. Math. 378, Amer. Math. Soc. (2005) 319 MR2159318
25	K M Goda, Centralisers in graph products of groups, PhD thesis, University of Newcastle-upon-Tyne (2006)
26	E R Green, Graph products of groups, PhD thesis, University of Leeds (1990)
27	M Gromov, Hyperbolic groups, from: "Essays in group theory" (editor S M Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
28	V Guirardel, Approximations of stable actions on $\mathbb{R}$–trees, Comment. Math. Helv. 73 (1998) 89 MR1610591
29	F Haglund, Isometries of $\mathrm{CAT}`(`0`)`$ cube complexes are semisimple, arXiv:0705.3386
30	F Haglund, Finite index subgroups of graph products, Geom. Dedicata 135 (2008) 167 MR2413337
31	F Haglund, D T Wise, Special cube complexes, Geom. Funct. Anal. 17 (2008) 1551 MR2377497
32	F Haglund, D T Wise, Coxeter groups are virtually special, Adv. Math. 224 (2010) 1890 MR2646113
33	S P Humphries, On representations of Artin groups and the Tits conjecture, J. Algebra 169 (1994) 847 MR1302120
34	M Kapovich, B Leeb, On asymptotic cones and quasi-isometry classes of fundamental groups of $3$–manifolds, Geom. Funct. Anal. 5 (1995) 582 MR1339818
35	A Kar, Asymptotically $\mathrm{CAT}(0)$ groups, Publ. Mat. 55 (2011) 67 MR2779576
36	A Kar, N Nikolov, Rank gradient and cost of Artin groups and their relatives, arXiv:1210.2873
37	O Kharlampovich, A Myasnikov, Irreducible affine varieties over a free group, I: Irreducibility of quadratic equations and Nullstellensatz, J. Algebra 200 (1998) 472 MR1610660
38	O Kharlampovich, A Myasnikov, Irreducible affine varieties over a free group, II: Systems in triangular quasiquadratic form and description of residually free groups, J. Algebra 200 (1998) 517 MR1610664
39	O Kharlampovich, A Myasnikov, Effective JSJ–decompositions, from: "Groups, languages, algorithms" (editor A V Borovik), Contemp. Math. 378, Amer. Math. Soc. (2005) 87 MR2159316
40	O Kharlampovich, A Myasnikov, Implicit function theorem over free groups, J. Algebra 290 (2005) 1 MR2154989
41	O Kharlampovich, A Myasnikov, Elementary theory of free nonabelian groups, J. Algebra 302 (2006) 451 MR2293770
42	M R Laurence, A generating set for the automorphism group of a graph group, J. London Math. Soc. 52 (1995) 318 MR1356145
43	Y Liu, Virtual cubulation of nonpositively curved graph manifolds, J. Topol. 6 (2013) 793 MR3145140
44	L Louder, Krull dimension for limit groups, Geom. Topol. 16 (2012) 219 MR2872582
45	J C Mayer, J Nikiel, L G Oversteegen, Universal spaces for $\mathbb{R}$–trees, Trans. Amer. Math. Soc. 334 (1992) 411 MR1081940
46	A Minasyan, Hereditary conjugacy separability of right-angled Artin groups and its applications, Groups Geom. Dyn. 6 (2012) 335 MR2914863
47	A Myasnikov, V N Remeslennikov, Algebraic geometry over groups, II: Logical foundations, J. Algebra 234 (2000) 225 MR1799485
48	D Osin, M Sapir, Universal tree-graded spaces and asymptotic cones, Internat. J. Algebra Comput. 21 (2011) 793 MR2827204
49	V N Remeslennikov, $\exists$–free groups, Siberian Math. J. 30 (1989) 193 MR1043446
50	J Roe, Lectures on coarse geometry, Univ. Lecture Series 31, Amer. Math. Soc. (2003) MR2007488
51	M Sageev, Ends of group pairs and nonpositively curved cube complexes, Proc. London Math. Soc. 71 (1995) 585 MR1347406
52	Z Sela, Diophantine geometry over groups, I: Makanin–Razborov diagrams, Publ. Math. Inst. Hautes Études Sci. (2001) 31 MR1863735
53	Z Sela, Diophantine geometry over groups, II: Completions, closures and formal solutions, Israel J. Math. 134 (2003) 173 MR1972179
54	Z Sela, Diophantine geometry over groups, VI: The elementary theory of a free group, Geom. Funct. Anal. 16 (2006) 707 MR2238945
55	A Sisto, Bilipschitz types of tree-graded spaces, arXiv:1010.4552
56	J Stallings, A finitely presented group whose $3$–dimensional integral homology is not finitely generated, Amer. J. Math. 85 (1963) 541 MR0158917
57	J Tits, A “theorem of Lie–Kolchin” for trees, from: "Contributions to algebra (collection of papers dedicated to Ellis Kolchin)" (editors H Bass, P J Cassidy, J Kovacic), Academic Press (1977) 377 MR0578488
58	H Wilton, Solutions to Bestvina & Feighn's exercises on limit groups, from: "Geometric and cohomological methods in group theory" (editors M R Bridson, P H Kropholler, I J Leary), London Math. Soc. Lecture Note Ser. 358, Cambridge Univ. Press (2009) 30 MR2605175