Volume 23, issue 6 (2019)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 8, 3511–3972
Issue 7, 3001–3510
Issue 6, 2483–2999
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Local topological rigidity of nongeometric $3$–manifolds

Filippo Cerocchi and Andrea Sambusetti

Geometry & Topology 23 (2019) 2899–2927
Bibliography
1 M T Anderson, L Rodríguez, Minimal surfaces and 3–manifolds of nonnegative Ricci curvature, Math. Ann. 284 (1989) 461 MR1001714
2 M Aschenbrenner, S Friedl, H Wilton, 3–manifold groups, 20, Eur. Math. Soc. (2015) MR3444187
3 J A Behrstock, W D Neumann, Quasi-isometric classification of graph manifold groups, Duke Math. J. 141 (2008) 217 MR2376814
4 J A Behrstock, W D Neumann, Quasi-isometric classification of non-geometric 3–manifold groups, J. Reine Angew. Math. 669 (2012) 101 MR2980453
5 L Bessières, G Besson, S Maillot, M Boileau, J Porti, Geometrisation of 3–manifolds, 13, Eur. Math. Soc. (2010) MR2683385
6 G Besson, G Courtois, S Gallot, Un lemme de Margulis sans courbure et ses applications, preprint (2003)
7 F Bonahon, Geometric structures on 3–manifolds, from: "Handbook of geometric topology" (editors R J Daverman, R B Sher), North-Holland (2002) 93 MR1886669
8 M Bucher, A Talambutsa, Exponential growth rates of free and amalgamated products, Israel J. Math. 212 (2016) 521 MR3505396
9 P Buser, H Karcher, Gromov’s almost flat manifolds, 81, Soc. Math. France (1981) 148 MR619537
10 J Cao, X Chen, Minimal volume and simplicial norm of visibility n–manifolds and compact 3–manifolds, preprint (2008) arXiv:0812.3353
11 F Cerocchi, Margulis lemma, entropy and free products, Ann. Inst. Fourier (Grenoble) 64 (2014) 1011 MR3330162
12 F Cerocchi, On the peripheral subgroups of irreducible 3–manifold groups and acylindrical splittings, preprint (2017) arXiv:1705.06124
13 F Cerocchi, A Sambusetti, Convergence of non-positively curved manifolds with acylindrical splittings, in preparation
14 F Cerocchi, A Sambusetti, Entropy and finiteness of groups with acylindrical splittings, preprint (2018) arXiv:1711.06210v2
15 J Cheeger, T H Colding, Lower bounds on Ricci curvature and the almost rigidity of warped products, Ann. of Math. 144 (1996) 189 MR1405949
16 J Cheeger, M Gromov, Collapsing Riemannian manifolds while keeping their curvature bounded, I, J. Differential Geom. 23 (1986) 309 MR852159
17 R Frigerio, J F Lafont, A Sisto, Rigidity of high dimensional graph manifolds, 372, Soc. Math. France (2015) MR3444648
18 K Fukaya, T Yamaguchi, The fundamental groups of almost non-negatively curved manifolds, Ann. of Math. 136 (1992) 253 MR1185120
19 M Gromov, Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. 56 (1982) 5 MR686042
20 M Gromov, Filling Riemannian manifolds, J. Differential Geom. 18 (1983) 1 MR697984
21 M Gromov, Metric structures for Riemannian and non-Riemannian spaces, Birkhäuser (2007) MR2307192
22 R S Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982) 255 MR664497
23 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
24 J Heber, G Knieper, H M Shah, Asymptotically harmonic spaces in dimension 3, Proc. Amer. Math. Soc. 135 (2007) 845 MR2262881
25 J Hempel, 3–manifolds, 86, Princeton Univ. Press (1976) MR0415619
26 W H Jaco, P B Shalen, Seifert fibered spaces in 3–manifolds, 220, Amer. Math. Soc. (1979) MR539411
27 K Johannson, Équivalences d’homotopie des variétés de dimension 3, C. R. Acad. Sci. Paris Sér. A-B 281 (1975) 1009 MR391096
28 K Johannson, Homotopy equivalences of 3–manifolds with boundaries, 761, Springer (1979) MR551744
29 I Kapovich, R Weidmann, Two-generated groups acting on trees, Arch. Math. (Basel) 73 (1999) 172 MR1705011
30 M Kapovich, Hyperbolic manifolds and discrete groups, 183, Birkhäuser (2001) MR1792613
31 M Kapovich, B Leeb, On asymptotic cones and quasi-isometry classes of fundamental groups of 3–manifolds, Geom. Funct. Anal. 5 (1995) 582 MR1339818
32 M Kapovich, B Leeb, Quasi-isometries preserve the geometric decomposition of Haken manifolds, Invent. Math. 128 (1997) 393 MR1440310
33 V Kapovitch, B Wilking, Structure of fundamental groups of manifolds with Ricci curvature bounded below, preprint (2011) arXiv:1105.5955
34 G Knieper, Spherical means on compact Riemannian manifolds of negative curvature, Differential Geom. Appl. 4 (1994) 361 MR1306567
35 B Leeb, 3–manifolds with(out) metrics of nonpositive curvature, Invent. Math. 122 (1995) 277 MR1358977
36 A Manning, Topological entropy for geodesic flows, Ann. of Math. 110 (1979) 567 MR554385
37 E E Moise, Affine structures in 3–manifolds, V : The triangulation theorem and Hauptvermutung, Ann. of Math. 56 (1952) 96 MR48805
38 D Müllner, Orientation reversal of manifolds, Algebr. Geom. Topol. 9 (2009) 2361 MR2558314
39 J Munkres, Obstructions to the smoothing of piecewise-differentiable homeomorphisms, Bull. Amer. Math. Soc. 65 (1959) 332 MR112150
40 J Munkres, Obstructions to the smoothing of piecewise-differentiable homeomorphisms, Ann. of Math. 72 (1960) 521 MR121804
41 W D Neumann, Graph 3–manifolds, splice diagrams, singularities, from: "Singularity theory" (editors D Chéniot, N Dutertre, C Murolo, D Trotman, A Pichon), World Sci. (2007) 787 MR2342940
42 K Ohshika, Teichmüller spaces of Seifert fibered manifolds with infinite π1, Topology Appl. 27 (1987) 75 MR910495
43 J P Otal, Le théorème d’hyperbolisation pour les variétés fibrées de dimension 3, 235, Soc. Math. France (1996) MR1402300
44 J P Otal, Thurston’s hyperbolization of Haken manifolds, from: "Surveys in differential geometry" (editors C C Hsiung, S T Yau), Surv. Diff. Geom. 3, International (1998) 77 MR1677888
45 P Papasoglu, K Whyte, Quasi-isometries between groups with infinitely many ends, Comment. Math. Helv. 77 (2002) 133 MR1898396
46 G Perelman, The entropy formula for the Ricci flow and its geometric applications, preprint (2002) arXiv:math/0211159
47 G Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds, preprint (2003) arXiv:math/0307245
48 G Perelman, Ricci flow with surgery on three-manifolds, preprint (2003) arXiv:math/0303109
49 G Reviron, Rigidité topologique sous l’hypothèse “entropie majorée” et applications, Comment. Math. Helv. 83 (2008) 815 MR2442964
50 A Sambusetti, Minimal entropy and simplicial volume, Manuscripta Math. 99 (1999) 541 MR1713806
51 A Sambusetti, On minimal entropy and stability, Geom. Dedicata 81 (2000) 261 MR1772208
52 R Schoen, S T Yau, Complete three-dimensional manifolds with positive Ricci curvature and scalar curvature, from: "Seminar on Differential Geometry" (editor S T Yau), Ann. of Math. Stud. 102, Princeton Univ. Press (1982) 209 MR645740
53 V Schroeder, H Shah, On 3–dimensional asymptotically harmonic manifolds, Arch. Math. (Basel) 90 (2008) 275 MR2391362
54 P Scott, The geometries of 3–manifolds, Bull. London Math. Soc. 15 (1983) 401 MR705527
55 Z Sela, Acylindrical accessibility for groups, Invent. Math. 129 (1997) 527 MR1465334
56 W X Shi, Complete noncompact three-manifolds with nonnegative Ricci curvature, J. Differential Geom. 29 (1989) 353 MR982179
57 T Soma, The Gromov invariant of links, Invent. Math. 64 (1981) 445 MR632984
58 C Sormani, G Wei, Hausdorff convergence and universal covers, Trans. Amer. Math. Soc. 353 (2001) 3585 MR1837249
59 G A Swarup, Two finiteness properties in 3–manifolds, Bull. London Math. Soc. 12 (1980) 296 MR576979
60 W P Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. 6 (1982) 357 MR648524
61 W P Thurston, Hyperbolic structures on 3–manifolds, I : Deformation of acylindrical manifolds, Ann. of Math. 124 (1986) 203 MR855294
62 W P Thurston, Hyperbolic structures on 3–manifolds, II : Surface groups and 3–manifolds which fiber over the circle, preprint (1986) arXiv:math/9801045
63 W P Thurston, Hyperbolic structures on 3–manifolds, III : Deformations of 3–manifolds with incompressible boundary, preprint (1986) arXiv:math/9801058
64 W P Thurston, Three-dimensional geometry and topology, I, 35, Princeton Univ. Press (1997) MR1435975
65 V G Turaev, Homeomorphisms of geometric three-dimensional manifolds, Mat. Zametki 43 (1988) 533 MR940851
66 W Tuschmann, Hausdorff convergence and the fundamental group, Math. Z. 218 (1995) 207 MR1318154
67 F Waldhausen, On irreducible 3–manifolds which are sufficiently large, Ann. of Math. 87 (1968) 56 MR224099
68 J H C Whitehead, Manifolds with transverse fields in euclidean space, Ann. of Math. 73 (1961) 154 MR124917
69 H Wilton, P Zalesskii, Profinite properties of graph manifolds, Geom. Dedicata 147 (2010) 29 MR2660565
70 S H Zhu, A finiteness theorem for Ricci curvature in dimension three, J. Differential Geom. 37 (1993) 711 MR1217167