Algebraic & Geometric Topology Volume 26, issue 5 (2026)

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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Homoclinic leaves, Hausdorff limits and homeomorphisms

Ian Biringer and Cyril Lecuire

Algebraic & Geometric Topology 26 (2026) 1803–1868

DOI: 10.2140/agt.2026.26.1803

Bibliography

1	I Agol, Tameness of hyperbolic 3-manifolds, (2004) arXiv:math/0405568
2	I Biringer, J Johnson, Y Minsky, Extending pseudo-Anosov maps into compression bodies, J. Topol. 6 (2013) 1019 MR3145149
3	I Biringer, N G Vlamis, Automorphisms of the compression body graph, J. Lond. Math. Soc., II. Ser. 95 (2017) 94
4	J S Birman, H M Hilden, On isotopies of homeomorphisms of Riemann surfaces, Ann. of Math. (2) 97 (1973) 424 MR325959
5	F Bonahon, Cobordism of automorphisms of surfaces, Ann. Sci. École Norm. Sup. (4) 16 (1983) 237 MR732345
6	B H Bowditch, Relatively hyperbolic groups, Internat. J. Algebra Comput. 22 (2012) 1250016 MR2922380
7	J F Brock, Continuity of Thurston’s length function, Geom. Funct. Anal. 10 (2000) 741 MR1791139
8	J F Brock, Iteration of mapping classes and limits of hyperbolic 3-manifolds, Invent. Math. 143 (2001) 523 MR1817644
9	J F Brock, R D Canary, Y N Minsky, The classification of Kleinian surface groups, II : The ending lamination conjecture, Ann. of Math. (2) 176 (2012) 1 MR2925381
10	J Brock, Y Minsky, H Namazi, J Souto, Bounded combinatorics and uniform models for hyperbolic 3-manifolds, J. Topol. 9 (2016) 451 MR3509970
11	D Calegari, D Gabai, Shrinkwrapping and the taming of hyperbolic 3-manifolds, J. Amer. Math. Soc. 19 (2006) 385 MR2188131
12	R D Canary, Algebraic convergence of Schottky groups, Trans. Amer. Math. Soc. 337 (1993) 235 MR1137257
13	R D Canary, Ends of hyperbolic 3-manifolds, J. Amer. Math. Soc. 6 (1993) 1 MR1166330
14	R D Canary, A covering theorem for hyperbolic 3-manifolds and its applications, Topology 35 (1996) 751 MR1396777
15	J W Cannon, C D Feustel, Essential embeddings of annuli and Möbius bands in 3-manifolds, Trans. Amer. Math. Soc. 215 (1976) 219 MR391094
16	A J Casson, S A Bleiler, Automorphisms of surfaces after Nielsen and Thurston, 9, Cambridge Univ. Press (1988) MR964685
17	A J Casson, C M Gordon, Reducing Heegaard splittings, Topology Appl. 27 (1987) 275 MR918537
18	A J Casson, D D Long, Algorithmic compression of surface automorphisms, Invent. Math. 81 (1985) 295 MR799268
19	M T Clay, C J Leininger, J Mangahas, The geometry of right-angled Artin subgroups of mapping class groups, Groups Geom. Dyn. 6 (2012) 249 MR2914860
20	V Erlandsson, M Gendulphe, I Pasquinelli, J Souto, Mapping class group orbit closures for non-orientable surfaces, Geom. Funct. Anal. 33 (2023) 637 MR4597639
21	B Farb, D Margalit, A primer on mapping class groups, 49, Princeton Univ. Press (2012) MR2850125
22	A Fathi, F Laudenbach, V Poenaru, Travaux de Thurston sur les surfaces : séminaire Orsay, 66-67, Soc. Math. France (1979) 284 MR568308
23	V Gadre, The limit set of the handlebody set has measure zero, (2011) arXiv:1105.2980
24	U Hamenstädt, Train tracks and the Gromov boundary of the complex of curves, from: "Spaces of Kleinian groups" (editors Y N Minsky, M Sakuma, C Series), London Math. Soc. Lecture Note Ser. 329, Cambridge Univ. Press (2006) 187 MR2258749
25	U Hamenstädt, Hyperbolic relatively hyperbolic graphs and disk graphs, Groups Geom. Dyn. 10 (2016) 365 MR3460340
26	U Hamenstädt, Asymptotic dimension and the disk graph, I, J. Topol. 12 (2019) 658 MR4072176
27	U Hamenstädt, Asymptotic dimension and the disk graph, II, J. Topol. 12 (2019) 675 MR3932938
28	G C Hruska, Relative hyperbolicity and relative quasiconvexity for countable groups, Algebr. Geom. Topol. 10 (2010) 1807 MR2684983
29	W Jaco, Lectures on three-manifold topology, 43, Amer. Math. Soc. (1980) MR565450
30	W H Jaco, P B Shalen, Seifert fibered spaces in 3-manifolds, 220, Amer. Math. Soc. (1979) MR539411
31	W Jeon, I Kim, K Ohshika, C Lecuire, Primitive stable representations of free Kleinian groups, Israel J. Math. 199 (2014) 841 MR3219560
32	K Johannson, Homotopy equivalences of 3-manifolds with boundaries, 761, Springer (1979) MR551744
33	M Kapovich, Hyperbolic manifolds and discrete groups, 183, Birkhäuser (2001) MR1792613
34	S P Kerckhoff, The measure of the limit set of the handlebody group, Topology 29 (1990) 27 MR1046623
35	I Kim, C Lecuire, K Ohshika, Convergence of freely decomposable Kleinian groups, Invent. Math. 204 (2016) 83 MR3480554
36	I Kim, M Lee, Separable-stable representations of a compression body, Topology Appl. 206 (2016) 171 MR3494440
37	E Klarreich, The boundary at infinity of the curve complex and the relative Teichmüller space, Groups Geom. Dyn. 16 (2022) 705 MR4502619
38	G Kleineidam, J Souto, Algebraic convergence of function groups, Comment. Math. Helv. 77 (2002) 244 MR1915041
39	M Lackenby, Attaching handlebodies to 3-manifolds, Geom. Topol. 6 (2002) 889 MR1943384
40	C Lecuire, Structures hyperboliques convexes sur les variétés de dimension 3, PhD thesis, École normale supérieure de Lyon (2004)
41	C Lecuire, An extension of the Masur domain, from: "Spaces of Kleinian groups" (editors Y N Minsky, M Sakuma, C Series), London Math. Soc. Lecture Note Ser. 329, Cambridge Univ. Press (2006) 49 MR2258744
42	C Lecuire, Plissage des variétés hyperboliques de dimension 3, Invent. Math. 164 (2006) 85 MR2207784
43	D D Long, Discs in compression bodies, Pacific J. Math. 122 (1986) 129 MR825228
44	J F Manning, The Bowditch boundary of (G,ℋ) when G is hyperbolic, (2015) arXiv:1504.03630
45	H Masur, Uniquely ergodic quadratic differentials, Comment. Math. Helv. 55 (1980) 255 MR576605
46	H Masur, Measured foliations and handlebodies, Ergodic Theory Dynam. Systems 6 (1986) 99 MR837978
47	H A Masur, Y N Minsky, Geometry of the complex of curves, I : Hyperbolicity, Invent. Math. 138 (1999) 103 MR1714338
48	H A Masur, Y N Minsky, Quasiconvexity in the curve complex, from: "In the tradition of Ahlfors and Bers, III" (editors W Abikoff, A Haas), Contemp. Math. 355, Amer. Math. Soc. (2004) 309 MR2145071
49	H Masur, S Schleimer, The geometry of the disk complex, J. Amer. Math. Soc. 26 (2013) 1 MR2983005
50	K Matsuzaki, M Taniguchi, Hyperbolic manifolds and Kleinian groups, Clarendon (1998) MR1638795
51	J McCarthy, Normalizers and centralizers of pseudo-anosov mapping classes, preprint (1982)
52	Y Minsky, The classification of Kleinian surface groups, I : Models and bounds, Ann. of Math. (2) 171 (2010) 1 MR2630036
53	M Mj, Cannon–Thurston maps for Kleinian groups, Forum Math. Pi 5 (2017) MR3652816
54	J W Morgan, On Thurston’s uniformization theorem for three-dimensional manifolds, from: "The Smith conjecture" (editors J W Morgan, H Bass), Pure Appl. Math. 112, Academic (1984) 37 MR758464
55	H Namazi, J Souto, Heegaard splittings and pseudo-Anosov maps, Geom. Funct. Anal. 19 (2009) 1195 MR2570321
56	J P Otal, Courants géodesique et surfaces, PhD thesis, Université Paris-Sud, Orsay (1989)
57	P Scott, Strong annulus and torus theorems and the enclosing property of characteristic submanifolds of 3-manifolds, Quart. J. Math. Oxford Ser. (2) 35 (1984) 485 MR767777
58	W P Thurston, The geometry and topology of three-manifolds, lecture notes (1979)
59	W P Thurston, Hyperbolic Structures on 3-manifolds, III : Deformations of 3-manifolds with incompressible boundary, (1998) arXiv:math/9801058
60	G S Walsh, The bumping set and the characteristic submanifold, Algebr. Geom. Topol. 14 (2014) 283 MR3158760