Geometry & Topology Volume 13, issue 3 (2009)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Geometric intersection number and analogues of the curve complex for free groups

Ilya Kapovich and Martin Lustig

Geometry & Topology 13 (2009) 1805–1833

DOI: 10.2140/gt.2009.13.1805

Bibliography

1	J. Behrstock, M Bestvina, M. Clay, Growth of intersection numbers for free group automorphisms arXiv:0806.4975
2	M Bestvina, M Feighn, Outer limits
3	M Bestvina, M Feighn, The topology at infinity of $\mathrm{Out}(F_n)$, Invent. Math. 140 (2000) 651 MR1760754
4	M Bestvina, M Feighn, M Handel, A hyperbolic $\mathrm{Out}(F_n)$–complex arXiv:0808.3730
5	M Bestvina, M Handel, Train tracks and automorphisms of free groups, Ann. of Math. $(2)$ 135 (1992) 1 MR1147956
6	F Bonahon, Bouts des variétés hyperboliques de dimension $3$, Ann. of Math. $(2)$ 124 (1986) 71 MR847953
7	F Bonahon, The geometry of Teichmüller space via geodesic currents, Invent. Math. 92 (1988) 139 MR931208
8	F Bonahon, Geodesic currents on negatively curved groups, from: "Arboreal group theory (Berkeley, CA, 1988)" (editor R C Alperin), Math. Sci. Res. Inst. Publ. 19, Springer (1991) 143 MR1105332
9	M M Cohen, M Lustig, Very small group actions on $\mathbf{R}$–trees and Dehn twist automorphisms, Topology 34 (1995) 575 MR1341810
10	T Coulbois, A Hilion, M Lustig, $\mathbb R$–trees and laminations for free groups. I. Algebraic laminations, J. Lond. Math. Soc. $(2)$ 78 (2008) 723 MR2456901
11	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. $(2)$ 78 (2008) 737 MR2456902
12	T Coulbois, A Hilion, M Lustig, $\mathbb R$–trees and laminations for free groups. III. Currents and dual $\mathbb R$–tree metrics, J. Lond. Math. Soc. $(2)$ 78 (2008) 755 MR2456903
13	M Culler, K Vogtmann, Moduli of graphs and automorphisms of free groups, Invent. Math. 84 (1986) 91 MR830040
14	S Francaviglia, Geodesic currents and length compactness for automorphisms of free groups, Trans. Amer. Math. Soc. 361 (2009) 161 MR2439402
15	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
16	É Ghys, P de la Harpe, editors, Sur les groupes hyperboliques d'après Mikhael Gromov, Progress in Math. 83, Birkhäuser (1990) MR1086648
17	V Guirardel, Dynamics of $\mathrm{Out}(F_n)$ on the boundary of outer space, Ann. Sci. École Norm. Sup. $(4)$ 33 (2000) 433 MR1832819
18	V Guirardel, C\oe ur et nombre d'intersection pour les actions de groupes sur les arbres, Ann. Sci. École Norm. Sup. $(4)$ 38 (2005) 847 MR2216833
19	U Hamenstädt, Subgroups of $\mathrm{Out}(F_n)$, Lecture at the workshop “Discrete groups and geometric structures" (2008)
20	A Hatcher, K Vogtmann, The complex of free factors of a free group, Quart. J. Math. Oxford Ser. $(2)$ 49 (1998) 459 MR1660045
21	J Hempel, $3$–manifolds as viewed from the curve complex, Topology 40 (2001) 631 MR1838999
22	V Kaimanovich, I Kapovich, P Schupp, The subadditive ergodic theorem and generic stretching factors for free group automorphisms, Israel J. Math. 157 (2007) 1 MR2342439
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 Sunik), Contemp. Math. 394, Amer. Math. Soc. (2006) 149 MR2216713
25	I Kapovich, Clusters, currents, and Whitehead's algorithm, Experiment. Math. 16 (2007) 67 MR2312978
26	I Kapovich, M Lustig, Domains of proper discontinuity on the boundary of Outer space arXiv:0902.4263
27	I Kapovich, M Lustig, Intersection form, laminations and currents on free groups, to appear in Geom. Funct. Anal. arXiv:math.GR/0711.4337
28	I Kapovich, M Lustig, Ping-pong and Outer space arXiv:0902.4017
29	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
30	I Kapovich, T Nagnibeda, The Patterson–Sullivan embedding and minimal volume entropy for outer space, Geom. Funct. Anal. 17 (2007) 1201 MR2373015
31	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
32	M Lustig, A generalized intersection form for free groups, Preprint (2004)
33	M Lustig, Conjugacy and centralizers for iwip automorphisms of free groups, from: "Geometric group theory" (editors G N Arzhantseva, L Bartholdi, J Burillo, E Ventura), Trends Math., Birkhäuser (2007) 197 MR2395795
34	R. Martin, Nonuniquely ergodic foliations of thin type, measured currents and automorphisms of free groups, PhD thesis, UCLA (1995)
35	H A Masur, Y N Minsky, Geometry of the complex of curves. I. Hyperbolicity, Invent. Math. 138 (1999) 103 MR1714338
36	F Paulin, The Gromov topology on $\mathbf{R}$–trees, Topology Appl. 32 (1989) 197 MR1007101
37	W Thurston, The geometry and topology of three-manifolds, Princeton Univ. Math. Dept. Lecture Notes (1979)
38	H Zieschang, E Vogt, H D Coldewey, Flächen und ebene diskontinuierliche Gruppen, Lecture Notes in Math. 122, Springer (1970) MR0262378