Geometry & Topology Volume 23, issue 1 (2019)

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

Ubiquitous quasi-Fuchsian surfaces in cusped hyperbolic

$3$ –manifolds

Daryl Cooper and David Futer

Geometry & Topology 23 (2019) 241–298

DOI: 10.2140/gt.2019.23.241

Bibliography

1	I Agol, Criteria for virtual fibering, J. Topol. 1 (2008) 269 MR2399130
2	I Agol, The virtual Haken conjecture, Doc. Math. 18 (2013) 1045 MR3104553
3	L V Ahlfors, Finitely generated Kleinian groups, Amer. J. Math. 86 (1964) 413 MR0167618
4	M D Baker, On boundary slopes of immersed incompressible surfaces, Ann. Inst. Fourier (Grenoble) 46 (1996) 1443 MR1427132
5	M Baker, D Cooper, Immersed, virtually-embedded, boundary slopes, Topology Appl. 102 (2000) 239 MR1745446
6	M Baker, D Cooper, A combination theorem for convex hyperbolic manifolds, with applications to surfaces in 3–manifolds, J. Topol. 1 (2008) 603 MR2417445
7	M D Baker, D Cooper, Conservative subgroup separability for surfaces with boundary, Algebr. Geom. Topol. 13 (2013) 115 MR3031638
8	M D Baker, D Cooper, Finite-volume hyperbolic 3–manifolds contain immersed quasi-Fuchsian surfaces, Algebr. Geom. Topol. 15 (2015) 1199 MR3342690
9	N Bergeron, D T Wise, A boundary criterion for cubulation, Amer. J. Math. 134 (2012) 843 MR2931226
10	L Bers, Inequalities for finitely generated Kleinian groups, J. Analyse Math. 18 (1967) 23 MR0229817
11	F Bonahon, Bouts des variétés hyperboliques de dimension 3, Ann. of Math. 124 (1986) 71 MR847953
12	J F Brock, K W Bromberg, On the density of geometrically finite Kleinian groups, Acta Math. 192 (2004) 33 MR2079598
13	R D Canary, A covering theorem for hyperbolic 3–manifolds and its applications, Topology 35 (1996) 751 MR1396777
14	S Choi, Geometric structures on orbifolds and holonomy representations, Geom. Dedicata 104 (2004) 161 MR2043960
15	D Cooper, D D Long, Some surface subgroups survive surgery, Geom. Topol. 5 (2001) 347 MR1825666
16	D Cooper, D D Long, A W Reid, Essential closed surfaces in bounded 3–manifolds, J. Amer. Math. Soc. 10 (1997) 553 MR1431827
17	D Cooper, D Long, S Tillmann, Deforming convex projective manifolds, Geom. Topol. 22 (2018) 1349 MR3780436
18	M Culler, P B Shalen, Varieties of group representations and splittings of 3–manifolds, Ann. of Math. 117 (1983) 109 MR683804
19	K Delp, D Hoffoss, J F Manning, Problems in groups, geometry, and three-manifolds, preprint (2015) arXiv:1512.04620
20	D Futer, J S Purcell, S Schleimer, Effective bilipschitz bounds on drilling and filling, in preparation
21	W M Goldman, Geometric structures on manifolds and varieties of representations, from: "Geometry of group representations" (editors W M Goldman, A R Magid), Contemp. Math. 74, Amer. Math. Soc. (1988) 169 MR957518
22	D Groves, J F Manning, Quasiconvexity and Dehn filling, preprint (2017) arXiv:1708.07968
23	F Haglund, D T Wise, Special cube complexes, Geom. Funct. Anal. 17 (2008) 1551 MR2377497
24	F Haglund, D T Wise, Coxeter groups are virtually special, Adv. Math. 224 (2010) 1890 MR2646113
25	J Hass, J H Rubinstein, S Wang, Boundary slopes of immersed surfaces in 3–manifolds, J. Differential Geom. 52 (1999) 303 MR1758298
26	A E Hatcher, On the boundary curves of incompressible surfaces, Pacific J. Math. 99 (1982) 373 MR658066
27	C D Hodgson, S P Kerckhoff, Universal bounds for hyperbolic Dehn surgery, Ann. of Math. 162 (2005) 367 MR2178964
28	C D Hodgson, S P Kerckhoff, The shape of hyperbolic Dehn surgery space, Geom. Topol. 12 (2008) 1033 MR2403805
29	G C Hruska, D T Wise, Finiteness properties of cubulated groups, Compos. Math. 150 (2014) 453 MR3187627
30	W Jaco, Lectures on three-manifold topology, 43, Amer. Math. Soc. (1980) MR565450
31	J Kahn, V Markovic, Immersing almost geodesic surfaces in a closed hyperbolic three manifold, Ann. of Math. 175 (2012) 1127 MR2912704
32	J Kahn, V Markovic, The good pants homology and the Ehrenpreis conjecture, Ann. of Math. 182 (2015) 1 MR3374956
33	J Kahn, A Wright, Nearly Fuchsian surface subgroups of finite covolume Kleinian groups, preprint (2018) arXiv:1809.07211
34	A D Magid, Deformation spaces of Kleinian surface groups are not locally connected, Geom. Topol. 16 (2012) 1247 MR2967052
35	J Maher, Virtually embedded boundary slopes, Topology Appl. 95 (1999) 63 MR1691932
36	J D Masters, X Zhang, Closed quasi-Fuchsian surfaces in hyperbolic knot complements, Geom. Topol. 12 (2008) 2095 MR2431017
37	J D Masters, X Zhang, Quasi-Fuchsian surfaces in hyperbolic link complements, preprint (2009) arXiv:0909.4501
38	A Minasyan, Separable subsets of GFERF negatively curved groups, J. Algebra 304 (2006) 1090 MR2264291
39	U Oertel, Boundaries of π₁–injective surfaces, Topology Appl. 78 (1997) 215 MR1454601
40	A Papadopoulos, Metric spaces, convexity and nonpositive curvature, 6, Eur. Math. Soc. (2005) MR2132506
41	P Przytycki, D T Wise, Mixed 3–manifolds are virtually special, J. Amer. Math. Soc. 31 (2018) 319 MR3758147
42	M Ratner, Raghunathan’s topological conjecture and distributions of unipotent flows, Duke Math. J. 63 (1991) 235 MR1106945
43	M Sageev, Ends of group pairs and non-positively curved cube complexes, Proc. London Math. Soc. 71 (1995) 585 MR1347406
44	M Sageev, CAT(0) cube complexes and groups, from: "Geometric group theory" (editors M Bestvina, M Sageev, K Vogtmann), IAS/Park City Math. Ser. 21, Amer. Math. Soc. (2014) 7 MR3329724
45	P Scott, Subgroups of surface groups are almost geometric, J. London Math. Soc. 17 (1978) 555 MR0494062
46	N A Shah, Closures of totally geodesic immersions in manifolds of constant negative curvature, from: "Group theory from a geometrical viewpoint" (editors É Ghys, A Haefliger, A Verjovsky), World Sci. (1991) 718 MR1170382
47	W P Thurston, The geometry and topology of three-manifolds, lecture notes (1979)
48	J Tidmore, Cocompact cubulations of mixed 3–manifolds, Groups Geom. Dyn. 12 (2018) 1429 MR3874647
49	F Waldhausen, On irreducible 3–manifolds which are sufficiently large, Ann. of Math. 87 (1968) 56 MR0224099
50	D T Wise, From riches to raags : 3–manifolds, right-angled Artin groups, and cubical geometry, 117, Amer. Math. Soc. (2012) MR2986461
51	D T Wise, The structure of groups with a quasiconvex hierarchy, preprint (2012)
52	Q Zhang, Boundary slopes of immersed surfaces in Haken manifolds, J. Knot Theory Ramifications 18 (2009) 591 MR2527678