Algebraic & Geometric Topology Volume 19, issue 3 (2019)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Ethics Statement

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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

DOI: 10.2140/agt.2019.19.1385

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(F_n), 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, ℝ–trees and laminations for free groups, I : Algebraic laminations, J. Lond. Math. Soc. 78 (2008) 723 MR2456901
13	T Coulbois, A Hilion, M Lustig, ℝ–trees and laminations for free groups, II : The dual lamination of an ℝ–tree, J. Lond. Math. Soc. 78 (2008) 737 MR2456902
14	T Coulbois, A Hilion, M Lustig, ℝ–trees and laminations for free groups, III : Currents and dual ℝ–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(F_n), 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(F_n) : 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(F_N), 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 F_n 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