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

Volume 26
Issue 6, 1965–2352
Issue 5, 1597–1963
Issue 4, 1229–1596
Issue 3, 825–1227
Issue 2, 411–824
Issue 1, 1–410

Volume 25, 9 issues

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
Low complexity among principal fully irreducible elements of $\mathrm{Out}(F_3)$

Naomi Andrew, Paige Hillen, Robert Alonzo Lyman and Catherine Eva Pfaff

Algebraic & Geometric Topology 26 (2026) 2157–2180
Bibliography
1 Y Algom-Kfir, I Kapovich, C Pfaff, Stable strata of geodesics in outer space, Int. Math. Res. Not. 2019 (2019) 4549 MR3984078
2 Y Algom-Kfir, K Rafi, Mapping tori of small dilatation expanding train-track maps, Topology Appl. 180 (2015) 44 MR3293265
3 M Bestvina, Geometry of outer space, from: "Geometric group theory" (editors M Bestvina, M Sageev, K Vogtmann), IAS/Park City Math. Ser. 21, Amer. Math. Soc. (2014) 173 MR3329728
4 M Bestvina, M Feighn, Outer limits, preprint (1994)
5 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
6 M Bestvina, M Handel, Train tracks and automorphisms of free groups, Ann. of Math. 135 (1992) 1 MR1147956
7 D W Boyd, The maximal modulus of an algebraic integer, Math. Comp. 45 (1985) 243 MR790657
8 J H Cho, J Y Ham, The minimal dilatation of a genus-two surface, Experiment. Math. 17 (2008) 257 MR2455699
9 T Coulbois, Free group automorphisms and train-track representative in Python/Sage, software package (2012–)
10 M Culler, K Vogtmann, Moduli of graphs and automorphisms of free groups, Invent. Math. 84 (1986) 91 MR830040
11 R Dickmann, G Domat, T Hill, S Kwak, C Ospina, P Patel, R Rechkin, Thurston’s theorem : entropy in dimension one, Math. Res. Lett. 31 (2024) 127 MR4795986
12 S Dowdall, I Kapovich, C J Leininger, Dynamics on free-by-cyclic groups, Geom. Topol. 19 (2015) 2801 MR3416115
13 S Dowdall, I Kapovich, C J Leininger, McMullen polynomials and Lipschitz flows for free-by-cyclic groups, J. Eur. Math. Soc. (JEMS) 19 (2017) 3253 MR3713041
14 M Feighn, M Handel, The recognition theorem for Out(Fn), Groups Geom. Dyn. 5 (2011) 39 MR2763779
15 S Francaviglia, A Martino, Metric properties of outer space, Publ. Mat. 55 (2011) 433 MR2839451
16 V Gadre, J Maher, The stratum of random mapping classes, Ergodic Theory Dynam. Systems 38 (2018) 2666 MR3846722
17 D Gagnier, C Pfaff, Taking the high-edge route of rank-3 outer space, Internat. J. Algebra Comput. 33 (2023) 1659 MR4683223
18 J Y Ham, W T Song, The minimum dilatation of pseudo-Anosov 5-braids, Experiment. Math. 16 (2007) 167 MR2339273
19 M Handel, L Mosher, Axes in outer space, 1004, Amer. Math. Soc. (2011) MR2858636
20 P Hillen, Latent symmetry of graphs and stretch factors in Out(Fr), Groups Geom. Dyn. (2025)
21 E Hironaka, Small dilatation mapping classes coming from the simplest hyperbolic braid, Algebr. Geom. Topol. 10 (2010) 2041 MR2728483
22 I Kapovich, Algorithmic detectability of iwip automorphisms, Bull. Lond. Math. Soc. 46 (2014) 279 MR3194747
23 I Kapovich, J Maher, C Pfaff, S J Taylor, Random outer automorphisms of free groups : attracting trees and their singularity structures, Trans. Amer. Math. Soc. 375 (2022) 525 MR4358675
24 I Kapovich, J Maher, C Pfaff, S J Taylor, Random trees in the boundary of outer space, Geom. Topol. 26 (2022) 127 MR4404876
25 E Lanneau, J L Thiffeault, On the minimum dilatation of braids on punctured discs, Geom. Dedicata 152 (2011) 165 MR2795241
26 E Lanneau, J L Thiffeault, On the minimum dilatation of pseudo-Anosov homeromorphisms on surfaces of small genus, Ann. Inst. Fourier (Grenoble) 61 (2011) 105 MR2828128
27 H Masur, Interval exchange transformations and measured foliations, Ann. of Math. 115 (1982) 169 MR644018
28 L Mosher, C Pfaff, Lone axes in outer space, Algebr. Geom. Topol. 16 (2016) 3385 MR3584262
29 C E Pfaff, Out(Fr) train track automata, I : Proper full fold decompositions, J. Topol. Anal.
30 C Pfaff, Constructing and classifying fully irreducible outer automorphisms of free groups, PhD thesis, Rutgers University (2012) MR3130948
31 C Pfaff, Ideal Whitehead graphs in Out(Fr), II : The complete graph in each rank, J. Homotopy Relat. Struct. 10 (2015) 275 MR3348263
32 C E Pfaff, Code for rank 3 principal automata constructions, software package (2026)
33 R K Skora, Deformations of length functions in groups, preprint (1989)
34 W T Song, K H Ko, J E Los, Entropies of braids, J. Knot Theory Ramifications 11 (2002) 647 MR1915500
35 J R Stallings, Topology of finite graphs, Invent. Math. 71 (1983) 551 MR695906
36 W P Thurston, Entropy in dimension one, from: "Frontiers in complex dynamics" (editors A Bonifant, M Lyubich, S Sutherland), Princeton Math. Ser. 51, Princeton Univ. Press (2014) 339 MR3289916
37 C C Tsang, X Zeng, Minimum dilatations of pseudo-Anosov braids, preprint (2024) arXiv:2412.01648
38 K Vogtmann, On the geometry of outer space, Bull. Amer. Math. Soc. (N.S.) 52 (2015) 27 MR3286480