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

Volume 29
Issue 7, 3345–3919
Issue 6, 2783–3343
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
The conjugacy problem for UPG elements of $\mathrm{Out}(F_n)$

Mark Feighn and Michael Handel

Geometry & Topology 29 (2025) 1693–1817
Bibliography
1 M Bestvina, N Brady, Morse theory and finiteness properties of groups, Invent. Math. 129 (1997) 445 MR1465330
2 M Bestvina, M Handel, Train tracks and automorphisms of free groups, Ann. of Math. 135 (1992) 1 MR1147956
3 M Bestvina, M Feighn, M Handel, Laminations, trees, and irreducible automorphisms of free groups, Geom. Funct. Anal. 7 (1997) 215 MR1445386
4 M Bestvina, M Feighn, M Handel, The Tits alternative for Out(Fn), I : Dynamics of exponentially-growing automorphisms, Ann. of Math. 151 (2000) 517 MR1765705
5 M Bestvina, M Feighn, M Handel, Solvable subgroups of Out(Fn) are virtually abelian, Geom. Dedicata 104 (2004) 71 MR2043955
6 M Bestvina, M Feighn, M Handel, The Tits alternative for Out(Fn), II : A Kolchin type theorem, Ann. of Math. 161 (2005) 1 MR2150382
7 M Bestvina, M Feighn, M Handel, A McCool Whitehead type theorem for finitely generated subgroups of Out(Fn), Ann. H. Lebesgue 6 (2023) 65 MR4593604
8 M R Bridson, H Wilton, On the difficulty of presenting finitely presentable groups, Groups Geom. Dyn. 5 (2011) 301 MR2782175
9 M M Cohen, M Lustig, The conjugacy problem for Dehn twist automorphisms of free groups, Comment. Math. Helv. 74 (1999) 179 MR1691946
10 D Cooper, Automorphisms of free groups have finitely generated fixed point sets, J. Algebra 111 (1987) 453 MR916179
11 F Dahmani, On suspensions and conjugacy of hyperbolic automorphisms, Trans. Amer. Math. Soc. 368 (2016) 5565 MR3458391
12 F Dahmani, On suspensions, and conjugacy of a few more automorphisms of free groups, from: "Hyperbolic geometry and geometric group theory", Adv. Stud. Pure Math. 73, Math. Soc. Japan (2017) 135 MR3728496
13 F Dahmani, N Touikan, Reducing the conjugacy problem for relatively hyperbolic automorphisms to peripheral components, preprint (2021) arXiv:2103.16602
14 F Dahmani, N Touikan, Unipotent linear suspensions of free groups, preprint (2023) arXiv:2305.11274
15 F Dahmani, S Francaviglia, A Martino, N Touikan, The conjugacy problem for Out(F3), Forum Math. Sigma 13 (2025) MR4863720
16 M Feighn, M Handel, The recognition theorem for Out(Fn), Groups Geom. Dyn. 5 (2011) 39 MR2763779
17 M Feighn, M Handel, Algorithmic constructions of relative train track maps and CTs, Groups Geom. Dyn. 12 (2018) 1159 MR3845002
18 D Gaboriau, A Jaeger, G Levitt, M Lustig, An index for counting fixed points of automorphisms of free groups, Duke Math. J. 93 (1998) 425 MR1626723
19 R Geoghegan, Topological methods in group theory, 243, Springer (2008) MR2365352
20 S M Gersten, On Whitehead’s algorithm, Bull. Amer. Math. Soc. 10 (1984) 281 MR733696
21 S M Gersten, Fixed points of automorphisms of free groups, Adv. Math. 64 (1987) 51 MR879856
22 M Handel, L Mosher, Axes in outer space, 1004, Amer. Math. Soc. (2011) MR2858636
23 M Handel, L Mosher, Subgroup decomposition in Out(Fn), 1280, Amer. Math. Soc. (2020) MR4089372
24 S Kalajdžievski, Automorphism group of a free group: centralizers and stabilizers, J. Algebra 150 (1992) 435 MR1176906
25 I Kapovich, N Benakli, Boundaries of hyperbolic groups, from: "Combinatorial and geometric group theory", Contemp. Math. 296, Amer. Math. Soc. (2002) 39 MR1921706
26 I Kapovich, H Short, Greenberg’s theorem for quasiconvex subgroups of word hyperbolic groups, Canad. J. Math. 48 (1996) 1224 MR1426902
27 S Krstić, M Lustig, K Vogtmann, An equivariant Whitehead algorithm and conjugacy for roots of Dehn twist automorphisms, Proc. Edinb. Math. Soc. 44 (2001) 117 MR1879214
28 J E Los, On the conjugacy problem for automorphisms of free groups, Topology 35 (1996) 779 MR1396778
29 M Lustig, Structure and conjugacy for automorphisms of free groups, I, preprint (2000)
30 M Lustig, Structure and conjugacy for automorphisms of free groups, II, preprint (2001)
31 M Lustig, Conjugacy and centralizers for iwip automorphisms of free groups, from: "Geometric group theory", Birkhäuser (2007) 197 MR2395795
32 R C Lyndon, P E Schupp, Combinatorial group theory, 89, Springer (1977) MR577064
33 W Magnus, A Karrass, D Solitar, Combinatorial group theory: presentations of groups in terms of generators and relations, Interscience (1966) MR207802
34 J McCool, Some finitely presented subgroups of the automorphism group of a free group, J. Algebra 35 (1975) 205 MR396764
35 M Rodenhausen, Centralisers of polynomially growing automorphisms of free groups, PhD thesis, Universität Bonn (2013)
36 Z Sela, The isomorphism problem for hyperbolic groups, I, Ann. of Math. 141 (1995) 217 MR1324134
37 J P Serre, Trees, Springer (1980) MR607504
38 J R Stallings, Topology of finite graphs, Invent. Math. 71 (1983) 551 MR695906
39 O Veblen, P Franklin, On matrices whose elements are integers, Ann. of Math. 23 (1921) 1 MR1502588
40 J H C Whitehead, On certain sets of elements in a free group, Proc. Lond. Math. Soc. 41 (1936) 48 MR1575455
41 J H C Whitehead, On equivalent sets of elements in a free group, Ann. of Math. 37 (1936) 782 MR1503309