Volume 13, issue 2 (2009)

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Equivariant Ricci flow with surgery and applications to finite group actions on geometric $3$–manifolds

Jonathan Dinkelbach and Bernhard Leeb

Geometry & Topology 13 (2009) 1129–1173
Bibliography
1 R Bamler, Ricci flow with surgery, PhD thesis, München (2007)
2 M Boileau, B Leeb, J Porti, Geometrization of $3$–dimensional orbifolds, Ann. of Math. $(2)$ 162 (2005) 195 MR2178962
3 E J Brody, The topological classification of the lens spaces, Ann. of Math. $(2)$ 71 (1960) 163 MR0116336
4 J Cheeger, D Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. of Math. $(2)$ 96 (1972) 413 MR0309010
5 T H Colding, W P Minicozzi II, Estimates for the extinction time for the Ricci flow on certain $3$–manifolds and a question of Perelman, J. Amer. Math. Soc. 18 (2005) 561 MR2138137
6 T H Colding, W P Minicozzi II, Width and finite extinction time of Ricci flow, Geom. Topol. 12 (2008) 2537
7 J Dinkelbach, Equivariant Ricci flow with surgery, PhD thesis, München (2008)
8 D B A Epstein, Curves on $2$–manifolds and isotopies, Acta Math. 115 (1966) 83 MR0214087
9 D Gromoll, W Meyer, On complete open manifolds of positive curvature, Ann. of Math. $(2)$ 90 (1969) 75 MR0247590
10 K Grove, H Karcher, How to conjugate $C^{1}$–close group actions, Math. Z. 132 (1973) 11 MR0356104
11 K Grove, K Shiohama, A generalized sphere theorem, Ann. Math. $(2)$ 106 (1977) 201 MR0500705
12 R S Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982) 255 MR664497
13 A Hatcher, Notes on basic $3$–manifold topology (2000)
14 M W Hirsch, S Smale, On involutions of the $3$–sphere, Amer. J. Math. 81 (1959) 893 MR0111044
15 B Kleiner, J Lott, Notes on Perelman's papers, Geom. Topol. 12 (2008) 2587
16 G R Livesay, Involutions with two fixed points on the three-sphere, Ann. of Math. $(2)$ 78 (1963) 582 MR0155323
17 W H Meeks III, P Scott, Finite group actions on $3$–manifolds, Invent. Math. 86 (1986) 287 MR856847
18 W H Meeks III, S T Yau, Group actions on $\mathbf{R}^{3}$, from: "The Smith conjecture (New York, 1979)", Pure Appl. Math. 112, Academic Press (1984) 167 MR758468
19 W Meyer, Toponogov's theorem and applications, Lecture notes (1989)
20 J Morgan, G Tian, Completion of the proof of the Geometrization Conjecture arXiv:0809.4040
21 J Morgan, G Tian, Ricci flow and the Poincaré conjecture, Clay Math. Monogr. 3, Amer. Math. Soc. (2007) MR2334563
22 G D Mostow, Quasi-conformal mappings in $n$–space and the rigidity of hyperbolic space forms, Inst. Hautes Études Sci. Publ. Math. (1968) 53 MR0236383
23 J Munkres, Differentiable isotopies on the $2$–sphere, Michigan Math. J. 7 (1960) 193 MR0144354
24 R S Palais, Equivalence of nearby differentiable actions of a compact group, Bull. Amer. Math. Soc. 67 (1961) 362 MR0130321
25 G Perelman, The entropy formula for the Ricci flow and its geometric applications arXiv:math.DG/0211159
26 G Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds arXiv:math.DG/0307245
27 G Perelman, Ricci flow with surgery on three-manifolds arXiv:math.DG/0303109
28 G Prasad, Strong rigidity of $\mathbf{Q}$–rank $1$ lattices, Invent. Math. 21 (1973) 255 MR0385005
29 P Scott, The geometries of $3$–manifolds, Bull. London Math. Soc. 15 (1983) 401 MR705527
30 J P Serre, Linear representations of finite groups, Graduate Texts in Math. 42, Springer (1977) MR0450380
31 W P Thurston, Three-manifolds with symmetry, Preprint
32 W P Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. $($N.S.$)$ 6 (1982) 357 MR648524
33 W P Thurston, Three-dimensional geometry and topology. Vol. 1 (editor S Levy), Princeton Math. Ser. 35, Princeton Univ. Press (1997) MR1435975