Flats in 3-manifolds
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 14 (2005) no. 3, pp. 459-499.
@article{AFST_2005_6_14_3_459_0,
     author = {Kapovich, Michael},
     title = {Flats in $3$-manifolds},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {459--499},
     publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 14},
     number = {3},
     year = {2005},
     mrnumber = {2172587},
     zbl = {1085.57003},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2005_6_14_3_459_0/}
}
TY  - JOUR
AU  - Kapovich, Michael
TI  - Flats in $3$-manifolds
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2005
SP  - 459
EP  - 499
VL  - 14
IS  - 3
PB  - Université Paul Sabatier, Institut de mathématiques
PP  - Toulouse
UR  - http://www.numdam.org/item/AFST_2005_6_14_3_459_0/
LA  - en
ID  - AFST_2005_6_14_3_459_0
ER  - 
%0 Journal Article
%A Kapovich, Michael
%T Flats in $3$-manifolds
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2005
%P 459-499
%V 14
%N 3
%I Université Paul Sabatier, Institut de mathématiques
%C Toulouse
%U http://www.numdam.org/item/AFST_2005_6_14_3_459_0/
%G en
%F AFST_2005_6_14_3_459_0
Kapovich, Michael. Flats in $3$-manifolds. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 14 (2005) no. 3, pp. 459-499. http://www.numdam.org/item/AFST_2005_6_14_3_459_0/

[Ba] Bass (H.). - Finitely generated subgroups of GL2 , In: "Smith Conjecture" , Acad. Press, p. 127-136 (1984). | MR | Zbl

[BF] Bestvina ( M.), Feighn (M.). - Stable actions of groups on real trees, Inv. Math., 121, F. 2, p. 287-322 (1995). | MR | Zbl

[BM] Bestvina ( M.), Mess (G.). - The boundary of negatively curved groups, Journal of AMS, 4, N 3, p. 469-481 (1991). | MR | Zbl

[BK1] Bonk (M. ), Kleiner (B.). - Rigidity for quasi-Möbius group actions, J. Differential Geom. vol. 61, no. 1, p. 81-106 (2002). | Zbl

[BK2] Bonk (M. ), Kleiner (B.). - Quasisymmetric parametrizations of two-dimensional metric spheres, Invent. Math. 150, no. 1, p. 127-183 (2002). | MR | Zbl

[BH] Bridson ( M.), Haefliger (A.). - "Metric spaces of non-positive curvature", Grundlehren der Mathematischen Wissenschaften , Vol. 319, Springer-Verlag (1999). | MR | Zbl

[B] Buyalo (S. ). - Euclidean planes in 3-dimensional manifolds of nonpositive curvature, Mat. Zametki, 43, p. 103-114 (1988). | MR | Zbl

[CJ] Casson (A. ), Jungreis (D.). - Convergence groups and Seifert fibered 3-manifolds, Inventiones Math., 118, F. 3, p. 441-456 (1994). | MR | Zbl

[Ca] Cannon (J. ). - The combinatorial Riemann mapping theorem, Acta Mathematica, 173, p. 155-234 (1994). | MR | Zbl

[CS] Cannon (J. ), Swensen (E.). - Recognizing constant curvature discrete groups in dimension 3, Trans. Amer. Math. Soc., 350, p. 809-849 (1998). | MR | Zbl

[E] Eberlein ( P.). - Geodesic flow on certain manifolds without conjugate points, Transaction of AMS, 167, p. 151-170 (1972). | MR | Zbl

[Ga1] Gabai (D. ). - Convergence groups are Fuchsian groups , Annals of Mathematics, 136, p. 447-510 (1992). | MR | Zbl

[Ga2] Gabai (D.). - Quasi-minimal semi-Euclidean laminations in 3-manifolds , In: "Surveys in differential geometry" , Vol. III (Cambridge, MA, 1996), Int. Press, Boston, MA , p. 195-242 (1988). | MR | Zbl

[Ga3] Gabai (D.). - A geometric and topological rigidity of hyperbolic 3-manifolds, Journ. of AMS, 10, p 37-74 (1997). | MR | Zbl

[Gh] Ghys (E.) , De La Harpe ( P.). - Infinite groups as geometric objects (after Gromov), In: "Ergodic Theory, Dynamics and Hyperbolic Groups", Oxford Sci. Publ., p. 299-314 (1991). | MR | Zbl

[Gri] Grigorchuk ( R.). - Growth degrees of p-groups and torsion-free groups, Math. USSR, Sb., 54, p. 185-205 (1985). | Zbl

[Gro1] Gromov ( M.). - Groups of polynomial growth and expanding maps, Publ. of IHES, 53, p. 53-73 (1981). | Numdam | MR | Zbl

[Gro2] Gromov (M.). - Hyperbolic groups, In: "Essays in Group Theory", Publications of MSRI, Vol. 8, p. 75-264 (1987). | MR | Zbl

[Gro3] Gromov (M.). - Asymptotic invariants of infinite groups, in "Geometric Group Theory", Vol. 2; London Math. Society Lecture Notes, 182, Cambridge Univ. Press (1993). | MR | Zbl

[He1] Hempel ( J.). - "3-manifolds", Annals of Math. Studies, Vol. 86, Princeton Univ. Press, (1976). | MR | Zbl

[He2] Hempel ( J.). - Residual finiteness for 3-manifolds . In: Annals of Math. Studies, Vol. 111, Princeton Univ. Press, p. 373-396 (1987). | MR | Zbl

[I] Imanishi ( H.). - On the theorem of Denjoy-Sacksteder for codimension one foliations without holonomy, J. Math. Kyoto Univ., 14, p. 607-634 (1974). | MR | Zbl

[K] Kapovich (M. ). - "Hyperbolic Manifolds and Discrete Groups", Birkhäuser (2001). | MR | Zbl

[KK1] Kapovich (M. ) , Kleiner ( B.). - Geometry of quasi-planes , Preprint (2004).

[KK2] Kapovich (M. ) , Kleiner ( B.). - Weak hyperbolization conjecture for 3-dimensional CAT(0) groups, Preprint (2004).

[KL] Kapovich ( M.), Leeb (B.), Quasi-isometries preserve the geometric decomposition of Haken manifolds, Inventiones Math , vol. 128, p. 393-416 (1997). | MR | Zbl

[KI] Kleiner (B. ). - Private communication.

[L] Long (D.). - Immersions and embeddings of totally geodesic surfaces , Bull. London Math. Soc., 19, p. 481-484 (1987). | MR | Zbl

[Mc] Mcmullen ( C.). - Iterations on Teichmüller space, Inventiones Math., 99, N 2, p. 425-454 (1989). | Zbl

[M1] Mess (G.). - The Seifert conjecture and groups which are coarse quasi- isometric to planes, Preprint (1990).

[M2] Mess (G.). - Private communication.

[Mor] Morgan ( J.). - On Thurston's Uniformization Theorem for Three-Dimensional Manifolds, In: "Smith Conjecture", Acad. Press, p. 37-136 (1984). | MR | Zbl

[MS1] Morgan ( J.), Shalen (P.). - Degenerations of hyperbolic structures, III: Actions of 3-manifold groups on trees and Thurston's compactness theorem, Ann. of Math., 127, p. 457-519 (1988). | MR | Zbl

[MS2] Morgan ( J.), Shalen (P.). - Free actions of surface groups on R-trees, Topology, vol. 30, no. 2, p. 143-154 (1991). | MR | Zbl

[MO] Mosher (L. ), Oertel (U.). - Spaces which are not negatively curved, Communications in Geometric Analysis, Communications in Analysis and Geometry, vol. 6, p. 67-140 (1998). | MR | Zbl

[O] Otal (J.-P. ). - Le théorème d'hyperbolisation pour les varietes fibrees de dimension trois, Astérisque, vol. 235 (1996). | Numdam | Zbl

[P1] Plante (J. ). - Foliations with measure preserving holonomy , Annals of Math., 102 N 2, p. 327-361 (1975). | MR | Zbl

[P2] Plante (J.) , Solvable groups acting on the real line, Transactions of AMS, 278, N 1 (1983). | MR | Zbl

[R] Rips (E.). - Group actions on R-trees, in preparation.

[Sc] Schroeder ( V. ). - Codimension one tori in manifolds of nonpositive curvature, Geom. Dedicata, 33, p. 251-265 (1990). | MR | Zbl

[Sch] Schwartz ( R.). - The quasi-isometry classification of hyperbolic lattices, Math. Publ. of IHES, Vol. 82, p. 133-168 (1995). | Numdam | MR | Zbl

[Sco] Scott (P. ). - A new proof of the annulus and torus theorems , Amer. Journal of Math., 102, p. 241-277 (1980). | MR | Zbl

[T] Thurston ( W.). - Hyperbolic structures on 3-manifolds, I, Annals of Math., 124, p. 203-246 (1986). | MR | Zbl

[Tu] Tukia (P. ). - Homeomorphic conjugates of fuchsian groups, J. Reine Angew. Math. 391, p. 1-54 (1988). | MR | Zbl

[VW] Van Den Dries (L.), Wilkie (A.J.). - On Gromov's theorem concerning groups of polynomial growth and elementary logic, Journ. of Algebra, Vol. 89, p. 349-374 (1984). | MR | Zbl