Geometry & Topology Volume 16, issue 1 (2012)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author Index

To Appear

Other MSP Journals

Ideal boundaries of pseudo-Anosov flows and uniform convergence groups with connections and applications to large scale geometry

Sérgio Fenley

Geometry & Topology 16 (2012) 1–110

DOI: 10.2140/gt.2012.16.1

Bibliography

1	T Barbot, Caractérisation des flots d'Anosov en dimension 3 par leurs feuilletages faibles, Ergodic Theory Dynam. Systems 15 (1995) 247 MR1332403
2	T Barbot, Mise en position optimale de tores par rapport à un flot d'Anosov, Comment. Math. Helv. 70 (1995) 113 MR1314942
3	T Barbot, Actions de groupes sur les $1$–variétés non séparées et feuilletages de codimension un, Ann. Fac. Sci. Toulouse Math. 7 (1998) 559 MR1693597
4	M Bestvina, M Feighn, A combination theorem for negatively curved groups, J. Differential Geom. 35 (1992) 85 MR1152226
5	M Bestvina, G Mess, The boundary of negatively curved groups, J. Amer. Math. Soc. 4 (1991) 469 MR1096169
6	C Bonatti, R Langevin, Un exemple de flot d'Anosov transitif transverse à un tore et non conjugué à une suspension, Ergodic Theory Dynam. Systems 14 (1994) 633 MR1304136
7	B H Bowditch, A topological characterisation of hyperbolic groups, J. Amer. Math. Soc. 11 (1998) 643 MR1602069
8	B H Bowditch, Convergence groups and configuration spaces, from: "Geometric group theory down under (Canberra, 1996)" (editors J Cossey, W D Neumann, M Shapiro), de Gruyter (1999) 23 MR1714838
9	D Calegari, $\mathbf R$–covered foliations of hyperbolic $3$–manifolds, Geom. Topol. 3 (1999) 137 MR1695533
10	D Calegari, The geometry of $\mathbf{R}$–covered foliations, Geom. Topol. 4 (2000) 457 MR1800151
11	D Calegari, Foliations with one-sided branching, Geom. Dedicata 96 (2003) 1 MR1956833
12	D Calegari, Promoting essential laminations, Invent. Math. 166 (2006) 583 MR2257392
13	D Calegari, N M Dunfield, Laminations and groups of homeomorphisms of the circle, Invent. Math. 152 (2003) 149 MR1965363
14	A Candel, Uniformization of surface laminations, Ann. Sci. École Norm. Sup. 26 (1993) 489 MR1235439
15	J W Cannon, E L Swenson, Recognizing constant curvature discrete groups in dimension $3$, Trans. Amer. Math. Soc. 350 (1998) 809 MR1458317
16	J W Cannon, W P Thurston, Group invariant Peano curves, Geom. Topol. 11 (2007) 1315 MR2326947
17	A J Casson, S A Bleiler, Automorphisms of surfaces after Nielsen and Thurston, London Math. Soc. Student Texts 9, Cambridge Univ. Press (1988) MR964685
18	A Casson, D Jungreis, Convergence groups and Seifert fibered $3$–manifolds, Invent. Math. 118 (1994) 441 MR1296353
19	M Coornaert, T Delzant, A Papadopoulos, Géométrie et théorie des groupes: Les groupes hyperboliques de Gromov, Lecture Notes in Math. 1441, Springer-Verlag (1990) MR1075994
20	A Fathi, F Laudenbach, V Poénaru, editors, Travaux de Thurston sur les surfaces, Astérisque 66–67, Soc. Math. France (1979) 284 MR568308
21	S R Fenley, Anosov flows in $3$–manifolds, Ann. of Math. 139 (1994) 79 MR1259365
22	S R Fenley, Quasigeodesic Anosov flows and homotopic properties of flow lines, J. Differential Geom. 41 (1995) 479 MR1331975
23	S R Fenley, Limit sets of foliations in hyperbolic $3$–manifolds, Topology 37 (1998) 875 MR1607756
24	S R Fenley, The structure of branching in Anosov flows of $3$–manifolds, Comment. Math. Helv. 73 (1998) 259 MR1611703
25	S R Fenley, Foliations with good geometry, J. Amer. Math. Soc. 12 (1999) 619 MR1674739
26	S R Fenley, Foliations, topology and geometry of $3$–manifolds: $\mathbf R$–covered foliations and transverse pseudo-Anosov flows, Comment. Math. Helv. 77 (2002) 415 MR1933786
27	S R Fenley, Pseudo-Anosov flows and incompressible tori, Geom. Dedicata 99 (2003) 61 MR1998929
28	S R Fenley, Geometry of foliations and flows I: Almost transverse pseudo-Anosov flows and asymptotic behavior of foliations, J. Differential Geom. 81 (2009) 1 MR2477891
29	S Fenley, L Mosher, Quasigeodesic flows in hyperbolic $3$–manifolds, Topology 40 (2001) 503 MR1838993
30	J Franks, R Williams, Anomalous Anosov flows, from: "Global theory of dynamical systems (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1979)" (editors Z Nitecki, C Robinson), Lecture Notes in Math. 819, Springer (1980) 158 MR591182
31	E M Freden, Negatively curved groups have the convergence property I, Ann. Acad. Sci. Fenn. Ser. A I Math. 20 (1995) 333 MR1346817
32	D Gabai, Convergence groups are Fuchsian groups, Ann. of Math. 136 (1992) 447 MR1189862
33	D Gabai, Problems in foliations and laminations, from: "Geometric topology (Athens, GA, 1993)" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 1 MR1470750
34	D Gabai, Quasi-minimal semi-Euclidean laminations in $3$–manifolds, from: "Surveys in differential geometry, Vol. III (Cambridge, MA, 1996)" (editor S T Yau), Int. Press (1998) 195 MR1677889
35	D Gabai, W H Kazez, Group negative curvature for $3$–manifolds with genuine laminations, Geom. Topol. 2 (1998) 65 MR1619168
36	D Gabai, U Oertel, Essential laminations in $3$–manifolds, Ann. of Math. 130 (1989) 41 MR1005607
37	F W Gehring, G J Martin, Discrete quasiconformal groups I, Proc. London Math. Soc. 55 (1987) 331 MR896224
38	É Ghys, P de la Harpe, editors, Sur les groupes hyperboliques d'après Mikhael Gromov, Progress in Math. 83, Birkhäuser (1990) MR1086648
39	S Goodman, S Shields, A condition for the stability of $\mathbf{R}$–covered on foliations of $3$–manifolds, Trans. Amer. Math. Soc. 352 (2000) 4051 MR1624178
40	M Gromov, Hyperbolic groups, from: "Essays in group theory" (editor S M Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
41	M Handel, Global shadowing of pseudo-Anosov homeomorphisms, Ergodic Theory Dynam. Systems 5 (1985) 373 MR805836
42	J Hempel, $3$–Manifolds, Ann. of Math. Studies 86, Princeton Univ. Press (1976) MR0415619
43	J L Kelley, General topology, Van Nostrand (1955) MR0070144
44	B S Mangum, Incompressible surfaces and pseudo-Anosov flows, Topology Appl. 87 (1998) 29 MR1626072
45	G Meigniez, Bouts d'un groupe opérant sur la droite, II. Applications à la topologie des feuilletages, Tohoku Math. J. 43 (1991) 473 MR1133863
46	J W Morgan, On Thurston's uniformization theorem for three-dimensional manifolds, from: "The Smith conjecture (New York, 1979)" (editors J W Morgan, H Bass), Pure Appl. Math. 112, Academic Press (1984) 37 MR758464
47	L Mosher, Dynamical systems and the homology norm of a $3$–manifold II, Invent. Math. 107 (1992) 243 MR1144424
48	L Mosher, Examples of quasi-geodesic flows on hyperbolic $3$–manifolds, from: "Topology '90 (Columbus, OH, 1990)" (editors B Apanasov, W D Neumann, A W Reid, L Siebenmann), Ohio State Univ. Math. Res. Inst. Publ. 1, de Gruyter (1992) 227 MR1184414
49	L Mosher, Laminations and flows transverse to finite depth foliations, Part I: Branched surfaces and dynamics, preprint (1996)
50	L Mosher, Laminations and flows transverse to finite depth foliations, Part II, in preparation
51	J R Munkres, Topology: a first course, Prentice-Hall (2000) MR0464128
52	J P Otal, Thurston's hyperbolization of Haken manifolds, from: "Surveys in differential geometry, Vol. III (Cambridge, MA, 1996)" (editor S T Yau), Int. Press (1998) 77 MR1677888
53	J P Otal, The hyperbolization theorem for fibered $3$–manifolds, SMF/AMS Texts and Monog. 7, Amer. Math. Soc. (2001) MR1855976
54	G Perelman, The entropy formulat for the Ricci flow and its geometric applications arXiv:math.DG/0211159
55	G Perelman, Ricci flow with surgery on $3$–manifolds arXiv:math.DG/0303109
56	G Perelman, Finite extinction time for the solutions to the Ricci flow in certain $3$–manifolds arXiv:math.DG/0307245
57	R Roberts, M Stein, Group actions on order trees, Topology Appl. 115 (2001) 175 MR1847462
58	W P Thurston, The geometry and topology of three-manifolds, Princeton Univ. Math. Dept. Lecture Notes (1979)
59	W P Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. 6 (1982) 357 MR648524
60	W P Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988) 417 MR956596
61	W P Thurston, Three-manifolds, foliations and circles I arXiv:math.GT/9712268
62	W P Thurston, Hyperbolic structures on $3$–manifolds II: Surface groups and $3$–manifolds that fiber over the circle arXiv:math.GT/9801045
63	P Tukia, Homeomorphic conjugates of Fuchsian groups, J. Reine Angew. Math. 391 (1988) 1 MR961162
64	P Tukia, Convergence groups and Gromov's metric hyperbolic spaces, New Zealand J. Math. 23 (1994) 157 MR1313451
65	P Tukia, Conical limit points and uniform convergence groups, J. Reine Angew. Math. 501 (1998) 71 MR1637829
66	F Waldhausen, On irreducible $3$–manifolds which are sufficiently large, Ann. of Math. 87 (1968) 56 MR0224099
67	R L Wilder, Topology of Manifolds, Amer. Math. Soc. Colloq. Publ. 32, Amer. Math. Soc. (1949) MR0029491