Volume 8, issue 3 (2004)

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

Volume 29
Issue 5, 2251–2782
Issue 4, 1693–2250
Issue 3, 1115–1691
Issue 2, 549–1114
Issue 1, 1–548

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
Limit groups and groups acting freely on $\mathbb{R}^n$–trees

Vincent Guirardel

Geometry & Topology 8 (2004) 1427–1470
Bibliography
1 H Bass, Group actions on non–Archimedean trees, from: "Arboreal group theory (Berkeley, CA, 1988)", Math. Sci. Res. Inst. Publ. 19, Springer (1991) 69 MR1105330
2 B Baumslag, Residually free groups, Proc. London Math. Soc. $(3)$ 17 (1967) 402 MR0215903
3 G Baumslag, On generalised free products, Math. Z. 78 (1962) 423 MR0140562
4 M Bestvina, M Feighn, Stable actions of groups on real trees, Invent. Math. 121 (1995) 287 MR1346208
5 N Bourbaki, Éléments de mathématique. Fasc XXX: Algèbre commutative. Chapitre 5: Entiers. Chapitre 6: Valuations, Actualités Scientifiques et Industrielles 1308, Hermann (1964) 207 MR0194450
6 K S Brown, Cohomology of groups, Graduate Texts in Mathematics 87, Springer (1982) MR672956
7 C Champetier, V Guirardel, Limit groups as limits of free groups, Israel J. Math. 146 (2005) 1 MR2151593
8 I M Chiswell, Nontrivial group actions on $\Lambda$–trees, Bull. London Math. Soc. 24 (1992) 277 MR1157264
9 I M Chiswell, Harrison's theorem for $\Lambda$–trees, Quart. J. Math. Oxford Ser. $(2)$ 45 (1994) 1 MR1269285
10 I M Chiswell, Introduction to $\Lambda$–trees, from: "Semigroups, formal languages and groups (York, 1993)", NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 466, Kluwer Acad. Publ. (1995) 255 MR1630624
11 I Chiswell, Introduction to $\Lambda$–trees, World Scientific Publishing Co. (2001) MR1851337
12 F Dahmani, Combination of convergence groups, Geom. Topol. 7 (2003) 933 MR2026551
13 D Gaboriau, G Levitt, F Paulin, Pseudogroups of isometries of $\mathbb{R}$ and Rips' theorem on free actions on $\mathbb{R}$–trees, Israel J. Math. 87 (1994) 403 MR1286836
14 A M Gaglione, D Spellman, Every “universally free” group is tree-free, from: "Group theory (Granville, OH, 1992)", World Sci. Publ., River Edge, NJ (1993) 149 MR1348896
15 A M Gaglione, D Spellman, Does Lyndon's length function imply the universal theory of free groups?, from: "The mathematical legacy of Wilhelm Magnus: groups, geometry and special functions (Brooklyn, NY, 1992)", Contemp. Math. 169, Amer. Math. Soc. (1994) 277 MR1292905
16 S Gross, Group actions on $\Lambda$–trees, PhD thesis, Hebrew University, Jerusalem (1998)
17 V Guirardel, Rips theory for actions of finitely generated groups on $\mathbb{R}$–trees, in preparation
18 N Harrison, Real length functions in groups, Trans. Amer. Math. Soc. 174 (1972) 77 MR0308283
19 S Jackson, L Q Zamboni, A note on a theorem of Chiswell, Proc. Amer. Math. Soc. 123 (1995) 2629 MR1277116
20 O Kharlampovich, A Myasnikov, Irreducible affine varieties over a free group I: Irreducibility of quadratic equations and Nullstellensatz, J. Algebra 200 (1998) 472 MR1610660
21 O Kharlampovich, A Myasnikov, Irreducible affine varieties over a free group II: Systems in triangular quasi-quadratic form and description of residually free groups, J. Algebra 200 (1998) 517 MR1610664
22 F V Kuhlmann, Value groups, residue fields, and bad places of rational function fields, Trans. Amer. Math. Soc. 356 (2004) 4559 MR2067134
23 R C Lyndon, The equation $a^{2}b^{2}=c^{2}$ in free groups, Michigan Math. J 6 (1959) 89 MR0103218
24 F Paulin, Sur la théorie élémentaire des groupes libres (d'après Sela), Astérisque (2004) 363 MR2111650
25 P H Pfander, Finitely generated subgroups of the free $\mathbb{Z}[t]$–group on two generators, from: "Model theory of groups and automorphism groups (Blaubeuren, 1995)", London Math. Soc. Lecture Note Ser. 244, Cambridge Univ. Press (1997) 166 MR1689871
26 V N Remeslennikov, $\exists$–free groups, Sibirsk. Mat. Zh. 30 (1989) 193 MR1043446
27 V N Remeslennikov, $\exists$–free groups as groups with a length function, Ukraïn. Mat. Zh. 44 (1992) 813 MR1185681
28 Z Sela, Acylindrical accessibility for groups, Invent. Math. 129 (1997) 527 MR1465334
29 Z Sela, A list of research problems
30 Z Sela, Diophantine geometry over groups I: Makanin–Razborov diagrams, Publ. Math. Inst. Hautes Études Sci. (2001) 31 MR1863735
31 M Urbański, L Zamboni, On free actions on $\Lambda$–trees, Math. Proc. Cambridge Philos. Soc. 113 (1993) 535 MR1207518
32 O Zariski, P Samuel, Commutative algebra Vol II, Springer (1975) MR0389876