Volume 9, issue 4 (2005)

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

Volume 23
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

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
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Other MSP Journals
The Grushko decomposition of a finite graph of finite rank free groups: an algorithm

Guo-An Diao and Mark Feighn

Geometry & Topology 9 (2005) 1835–1880
Bibliography
1 H Bass, Some remarks on group actions on trees, Comm. Algebra 4 (1976) 1091 MR0419616
2 M Bestvina, M Feighn, Outer limits, preprint (1994)
3 M Bestvina, M Feighn, A combination theorem for negatively curved groups, J. Differential Geom. 35 (1992) 85 MR1152226
4 M Bestvina, M Feighn, Bounding the complexity of simplicial group actions on trees, Invent. Math. 103 (1991) 449 MR1091614
5 M R Bridson, A Haefliger, Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer (1999) MR1744486
6 M R Bridson, D T Wise, $\scr V\scr H$ complexes, towers and subgroups of $F\times F$, Math. Proc. Cambridge Philos. Soc. 126 (1999) 481 MR1684244
7 P Brinkmann, Splittings of mapping tori of free group automorphisms, Geom. Dedicata 93 (2002) 191 MR1934698
8 D E Cohen, Combinatorial group theory: a topological approach, London Mathematical Society Student Texts 14, Cambridge University Press (1989) MR1020297
9 G A Diao, Is a graph of finitely generated free groups free? An algorithm (2003)
10 M Feighn, M Handel, Mapping tori of free group automorphisms are coherent, Ann. of Math. $(2)$ 149 (1999) 1061 MR1709311
11 K Fujiwara, P Papasoglu, JSJ-decompositions of finitely presented groups and complexes of groups, Geom. Funct. Anal. 16 (2006) 70 MR2221253
12 R Geoghegan, M L Mihalik, M Sapir, D T Wise, Ascending HNN extensions of finitely generated free groups are Hopfian, Bull. London Math. Soc. 33 (2001) 292 MR1817768
13 V Gerasimov, Detecting connectedness of the boundary of a hyperbolic group, preprint (1999)
14 S M Gersten, On Whitehead's algorithm, Bull. Amer. Math. Soc. $($N.S.$)$ 10 (1984) 281 MR733696
15 I A Grushko, On generators of a free product of groups (1940) 169
16 A Hatcher, Algebraic topology, Cambridge University Press (2002) MR1867354
17 W Jaco, D Letscher, J H Rubinstein, Algorithms for essential surfaces in 3–manifolds, from: "Topology and geometry: commemorating SISTAG", Contemp. Math. 314, Amer. Math. Soc. (2002) 107 MR1941626
18 S Kalajdžievski, Automorphism group of a free group: centralizers and stabilizers, J. Algebra 150 (1992) 435 MR1176906
19 O Kharlampovich, A Myasnikov, Irreducible affine varieties over a free group I: Irreducibility of quadratic equations and Nullstellensatz, J. Algebra 200 (1998) 472 MR1610660
20 O Kharlampovich, A G Myasnikov, Effective JSJ decompositions, from: "Groups, languages, algorithms", Contemp. Math. 378, Amer. Math. Soc. (2005) 87 MR2159316
21 R C Lyndon, P E Schupp, Combinatorial group theory, Classics in Mathematics, Springer (2001) MR1812024
22 C F Miller III, On group-theoretic decision problems and their classification, Annals of Mathematics Studies 68, Princeton University Press (1971) MR0310044
23 E Rips, Z Sela, Cyclic splittings of finitely presented groups and the canonical JSJ decomposition, Ann. of Math. $(2)$ 146 (1997) 53 MR1469317
24 Z Sela, Diophantine geometry over groups I: Makanin–Razborov diagrams, Publ. Math. Inst. Hautes Études Sci. (2001) 31 MR1863735
25 J P Serre, Trees, Springer Monographs in Mathematics, Springer (2003) MR1954121
26 A Shenitzer, Decomposition of a group with a single defining relation into a free product, Proc. Amer. Math. Soc. 6 (1955) 273 MR0069174
27 J R Stallings, Topology of finite graphs, Invent. Math. 71 (1983) 551 MR695906
28 J R Stallings, Foldings of $G$–trees, from: "Arboreal group theory (Berkeley, CA, 1988)", Math. Sci. Res. Inst. Publ. 19, Springer (1991) 355 MR1105341
29 G A Swarup, Decompositions of free groups, J. Pure Appl. Algebra 40 (1986) 99 MR825183
30 J H C Whitehead, On certain sets of elements in a free group (1936) 48
31 J H C Whitehead, On equivalent sets of elements in a free group, Ann. of Math. $(2)$ 37 (1936) 782 MR1503309