Volume 19, issue 3 (2019)

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

Volume 24
Issue 9, 4731–5219
Issue 8, 4139–4730
Issue 7, 3571–4137
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

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
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Hyperbolic extensions of free groups from atoroidal ping-pong

Caglar Uyanik

Algebraic & Geometric Topology 19 (2019) 1385–1411
Bibliography
1 M Bestvina, M Feighn, A combination theorem for negatively curved groups, J. Differential Geom. 35 (1992) 85 MR1152226
2 M Bestvina, M Feighn, Hyperbolicity of the complex of free factors, Adv. Math. 256 (2014) 104 MR3177291
3 M Bestvina, M Feighn, Subfactor projections, J. Topol. 7 (2014) 771 MR3252963
4 M Bestvina, M Feighn, M Handel, Laminations, trees, and irreducible automorphisms of free groups, Geom. Funct. Anal. 7 (1997) 215 MR1445386
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 F Bonahon, Geodesic currents on negatively curved groups, from: "Arboreal group theory" (editor R C Alperin), Math. Sci. Res. Inst. Publ. 19, Springer (1991) 143 MR1105332
8 P Brinkmann, Hyperbolic automorphisms of free groups, Geom. Funct. Anal. 10 (2000) 1071 MR1800064
9 M Clay, A Pettet, Relative twisting in outer space, J. Topol. Anal. 4 (2012) 173 MR2949239
10 M Clay, C Uyanik, Simultaneous construction of hyperbolic isometries, Pacific J. Math. 294 (2018) 71 MR3743366
11 D Cooper, Automorphisms of free groups have finitely generated fixed point sets, J. Algebra 111 (1987) 453 MR916179
12 T Coulbois, A Hilion, M Lustig, –trees and laminations for free groups, I : Algebraic laminations, J. Lond. Math. Soc. 78 (2008) 723 MR2456901
13 T Coulbois, A Hilion, M Lustig, –trees and laminations for free groups, II : The dual lamination of an –tree, J. Lond. Math. Soc. 78 (2008) 737 MR2456902
14 T Coulbois, A Hilion, M Lustig, –trees and laminations for free groups, III : Currents and dual –tree metrics, J. Lond. Math. Soc. 78 (2008) 755 MR2456903
15 S Dowdall, S J Taylor, The co-surface graph and the geometry of hyperbolic free group extensions, J. Topol. 10 (2017) 447 MR3653318
16 S Dowdall, S J Taylor, Hyperbolic extensions of free groups, Geom. Topol. 22 (2018) 517 MR3720349
17 B Farb, L Mosher, Convex cocompact subgroups of mapping class groups, Geom. Topol. 6 (2002) 91 MR1914566
18 M Feighn, M Handel, The recognition theorem for Out(Fn), Groups Geom. Dyn. 5 (2011) 39 MR2763779
19 R Gupta, Relative currents, Conform. Geom. Dyn. 21 (2017) 319 MR3713836
20 U Hamenstaedt, Word hyperbolic extensions of surface groups, preprint (2005) arXiv:math/0505244
21 M Handel, L Mosher, Subgroup decomposition in Out(Fn) : research announcement and introduction, preprint (2013) arXiv:1302.2681
22 C Horbez, A short proof of Handel and Mosher’s alternative for subgroups of Out(FN), Groups Geom. Dyn. 10 (2016) 709 MR3513113
23 I Kapovich, The frequency space of a free group, Internat. J. Algebra Comput. 15 (2005) 939 MR2197815
24 I Kapovich, Currents on free groups, from: "Topological and asymptotic aspects of group theory" (editors R Grigorchuk, M Mihalik, M Sapir, Z Šunik), Contemp. Math. 394, Amer. Math. Soc. (2006) 149 MR2216713
25 I Kapovich, M Lustig, Ping-pong and outer space, J. Topol. Anal. 2 (2010) 173 MR2652906
26 R P Kent IV, C J Leininger, Shadows of mapping class groups: capturing convex cocompactness, Geom. Funct. Anal. 18 (2008) 1270 MR2465691
27 G Levitt, M Lustig, Irreducible automorphisms of Fn have north-south dynamics on compactified outer space, J. Inst. Math. Jussieu 2 (2003) 59 MR1955207
28 M Lustig, C Uyanik, North–south dynamics of hyperbolic free group automorphisms on the space of currents, J. Topol. Anal. (2017)
29 M Lustig, C Uyanik, Perron–Frobenius theory and frequency convergence for reducible substitutions, Discrete Contin. Dyn. Syst. 37 (2017) 355 MR3583482
30 R Martin, Non-uniquely ergodic foliations of thin-type, measured currents and automorphisms of free groups, PhD thesis, University of California, Los Angeles (1995) MR2693216
31 L Mosher, A hyperbolic-by-hyperbolic hyperbolic group, Proc. Amer. Math. Soc. 125 (1997) 3447 MR1443845
32 M Queffélec, Substitution dynamical systems—spectral analysis, 1294, Springer (2010) MR2590264
33 S J Taylor, A note on subfactor projections, Algebr. Geom. Topol. 14 (2014) 805 MR3159971
34 S J Taylor, G Tiozzo, Random extensions of free groups and surface groups are hyperbolic, Int. Math. Res. Not. 2016 (2016) 294 MR3514064
35 C Uyanik, Dynamics of hyperbolic iwips, Conform. Geom. Dyn. 18 (2014) 192 MR3273532
36 C Uyanik, Generalized north-south dynamics on the space of geodesic currents, Geom. Dedicata 177 (2015) 129 MR3370027