Algebraic & Geometric Topology Volume 12, issue 3 (2012)

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Spectral rigidity of automorphic orbits in free groups

Mathieu Carette, Stefano Francaviglia, Ilya Kapovich and Armando Martino

Algebraic & Geometric Topology 12 (2012) 1457–1486

DOI: 10.2140/agt.2012.12.1457

Bibliography

1	M Bestvina, M Feighn, Hyperbolicity of the complex of free factors arXiv:1107.3308
2	M Bestvina, M Feighn, Outer limits, preprint (1993)
3	M Bestvina, M Feighn, A hyperbolic $\mathrm{Out}(F_n)$–complex, Groups Geom. Dyn. 4 (2010) 31 MR2566300
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 Handel, Train tracks and automorphisms of free groups, Ann. of Math. 135 (1992) 1 MR1147956
6	F Bonahon, Bouts des variétés hyperboliques de dimension 3, Ann. of Math. 124 (1986) 71 MR847953
7	F Bonahon, The geometry of Teichmüller space via geodesic currents, Invent. Math. 92 (1988) 139 MR931208
8	M R Bridson, K Vogtmann, The symmetries of outer space, Duke Math. J. 106 (2001) 391 MR1813435
9	M R Bridson, K Vogtmann, Automorphism groups of free groups, surface groups and free abelian groups, from: "Problems on mapping class groups and related topics", Proc. Sympos. Pure Math. 74, Amer. Math. Soc. (2006) 301 MR2264548
10	I Chiswell, Introduction to $\Lambda$–trees, World Scientific Publishing Co. (2001) MR1851337
11	M Clay, A Pettet, Currents twisting and nonsingular matrices, Comment. Math. Helv. (to appear)
12	M M Cohen, M Lustig, Very small group actions on $\mathbb{R}$–trees and Dehn twist automorphisms, Topology 34 (1995) 575 MR1341810
13	M M Cohen, M Lustig, M Steiner, $\mathbb{R}$–tree actions are not determined by the translation lengths of finitely many elements, from: "Arboreal group theory (Berkeley, CA, 1988)", Math. Sci. Res. Inst. Publ. 19, Springer (1991) 183 MR1105334
14	M Cohen, W Metzler, A Zimmermann, What does a basis of $F(a, b)$ look like?, Math. Ann. 257 (1981) 435 MR639577
15	T Coulbois, A Hilion, M Lustig, $\mathbb{R}$–trees and laminations for free groups I: Algebraic laminations, J. Lond. Math. Soc. 78 (2008) 723 MR2456901
16	T Coulbois, A Hilion, M Lustig, $\mathbb{R}$–trees and laminations for free groups II: The dual lamination of an $\mathbb{R}$–tree, J. Lond. Math. Soc. 78 (2008) 737 MR2456902
17	C B Croke, Rigidity for surfaces of nonpositive curvature, Comment. Math. Helv. 65 (1990) 150 MR1036134
18	C B Croke, Rigidity theorems in Riemannian geometry, from: "Geometric methods in inverse problems and PDE control", IMA Vol. Math. Appl. 137, Springer (2004) 47 MR2169902
19	C B Croke, P Eberlein, B Kleiner, Conjugacy and rigidity for nonpositively curved manifolds of higher rank, Topology 35 (1996) 273 MR1380497
20	C Croke, A Fathi, J Feldman, The marked length-spectrum of a surface of nonpositive curvature, Topology 31 (1992) 847 MR1191384
21	M Culler, Finite groups of outer automorphisms of a free group, from: "Contributions to group theory", Contemp. Math. 33, Amer. Math. Soc. (1984) 197 MR767107
22	M Culler, J W Morgan, Group actions on $\mathbb{R}$–trees, Proc. London Math. Soc. 55 (1987) 571 MR907233
23	M Culler, K Vogtmann, Moduli of graphs and automorphisms of free groups, Invent. Math. 84 (1986) 91 MR830040
24	M Culler, K Vogtmann, The boundary of outer space in rank two, from: "Arboreal group theory (Berkeley, CA, 1988)", Math. Sci. Res. Inst. Publ. 19, Springer (1991) 189 MR1105335
25	F Dal’Bo, I Kim, Marked length rigidity for symmetric spaces, Comment. Math. Helv. 77 (2002) 399 MR1915048
26	M Duchin, C J Leininger, K Rafi, Length spectra and degeneration of flat metrics, Invent. Math. 182 (2010) 231 MR2729268
27	A Fathi, F Laudenbach, V Poenaru, Travaux de Thurston sur les surfaces, Astérisque 66, Société Mathématique de France (1979) 284 MR568308
28	S Francaviglia, Geodesic currents and length compactness for automorphisms of free groups, Trans. Amer. Math. Soc. 361 (2009) 161 MR2439402
29	S Francaviglia, A Martino, Metric properties of outer space, Publ. Mat. 55 (2011) 433 MR2839451
30	V Guirardel, Approximations of stable actions on $\mathbb{R}$–trees, Comment. Math. Helv. 73 (1998) 89 MR1610591
31	V Guirardel, Dynamics of $\mathrm{Out}(F_n)$ on the boundary of outer space, Ann. Sci. École Norm. Sup. 33 (2000) 433 MR1832819
32	U Hamenstädt, Invariant Radon measures on measured lamination space, Invent. Math. 176 (2009) 223 MR2495764
33	M Handel, L Mosher, Subgroup classification in $\mathrm{Out}(F_n)$ arXiv:0908.1255
34	S Hersonsky, F Paulin, On the rigidity of discrete isometry groups of negatively curved spaces, Comment. Math. Helv. 72 (1997) 349 MR1476054
35	I Kapovich, The frequency space of a free group, Internat. J. Algebra Comput. 15 (2005) 939 MR2197815
36	I Kapovich, Currents on free groups, from: "Topological and asymptotic aspects of group theory" (editors R Grigorchuk, M Mihalik, M Sapir, Z Sunik), Contemp. Math. 394, Amer. Math. Soc. (2006) 149 MR2216713
37	I Kapovich, Clusters, currents, and Whitehead's algorithm, Experiment. Math. 16 (2007) 67 MR2312978
38	I Kapovich, Random length-spectrum rigidity for free groups, Proc. Amer. Math. Soc. 140 (2012) 1549 MR2869139
39	I Kapovich, M Lustig, The actions of $\mathrm{Out}(F_k)$ on the boundary of outer space and on the space of currents: minimal sets and equivariant incompatibility, Ergodic Theory Dynam. Systems 27 (2007) 827 MR2322181
40	I Kapovich, M Lustig, Geometric intersection number and analogues of the curve complex for free groups, Geom. Topol. 13 (2009) 1805 MR2496058
41	I Kapovich, M Lustig, Domains of proper discontinuity on the boundary of outer space, Illinois J. Math. 54 (2010) 89 MR2776986
42	I Kapovich, M Lustig, Intersection form, laminations and currents on free groups, Geom. Funct. Anal. 19 (2010) 1426 MR2585579
43	I Kapovich, M Lustig, Stabilizers of $\mathbb{R}$–trees with free isometric actions of $F_N$, J. Group Theory 14 (2011) 673 MR2831965
44	I Kapovich, T Nagnibeda, The Patterson–Sullivan embedding and minimal volume entropy for outer space, Geom. Funct. Anal. 17 (2007) 1201 MR2373015
45	I Kapovich, T Nagnibeda, Geometric entropy of geodesic currents on free groups, from: "Dynamical numbers—interplay between dynamical systems and number theory", Contemp. Math. 532, Amer. Math. Soc. (2010) 149 MR2762139
46	I Kapovich, T Nagnibeda, Generalized geodesic currents on free groups arXiv:1105.5742
47	I Kim, Ergodic theory and rigidity on the symmetric space of non-compact type, Ergodic Theory Dynam. Systems 21 (2001) 93 MR1826662
48	I Kim, Marked length rigidity of rank one symmetric spaces and their product, Topology 40 (2001) 1295 MR1867246
49	I Kim, Rigidity on symmetric spaces, Topology 43 (2004) 393 MR2052969
50	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
51	J P Otal, Le spectre marqué des longueurs des surfaces à courbure négative, Ann. of Math. 131 (1990) 151 MR1038361
52	F Paulin, The Gromov topology on $\mathbb{R}$–trees, Topology Appl. 32 (1989) 197 MR1007101
53	B Ray, Non-rigidity of cyclic automorphic orbits in free groups, Int. J. Alg. Comp. 22 (2012) 1250021
54	J Smillie, K Vogtmann, Length functions and outer space, Michigan Math. J. 39 (1992) 485 MR1182503
55	K Vogtmann, What is$\dots$outer space?, Notices Amer. Math. Soc. 55 (2008) 784 MR2436509
56	B Zimmermann, Über Homöomorphismen $n$–dimensionaler Henkelkörper und endliche Erweiterungen von Schottky–Gruppen, Comment. Math. Helv. 56 (1981) 474 MR639363