Flats in 3-manifolds

Michael Kapovich

Annales de la Faculté des sciences de Toulouse : Mathématiques (2005)

  • Volume: 14, Issue: 3, page 459-499
  • ISSN: 0240-2963

How to cite

top

Kapovich, Michael. "Flats in 3-manifolds." Annales de la Faculté des sciences de Toulouse : Mathématiques 14.3 (2005): 459-499. <http://eudml.org/doc/73654>.

@article{Kapovich2005,
author = {Kapovich, Michael},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {flats; hyperbolization conjecture; non-positive curvature},
language = {eng},
number = {3},
pages = {459-499},
publisher = {Université Paul Sabatier, Institut de Mathématiques},
title = {Flats in 3-manifolds},
url = {http://eudml.org/doc/73654},
volume = {14},
year = {2005},
}

TY - JOUR
AU - Kapovich, Michael
TI - Flats in 3-manifolds
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 2005
PB - Université Paul Sabatier, Institut de Mathématiques
VL - 14
IS - 3
SP - 459
EP - 499
LA - eng
KW - flats; hyperbolization conjecture; non-positive curvature
UR - http://eudml.org/doc/73654
ER -

References

top
  1. [Ba] Bass ( H.). - Finitely generated subgroups of GL2 , In: "Smith Conjecture" , Acad. Press, p. 127-136 (1984). Zbl0599.57003MR758465
  2. [BF] Bestvina ( M.), Feighn ( M.). — Stable actions of groups on real trees, Inv. Math., 121, F. 2, p. 287-322 (1995). Zbl0837.20047MR1346208
  3. [BM] Bestvina ( M.), Mess ( G.). — The boundary of negatively curved groups, Journal of AMS, 4, N 3, p. 469-481 (1991). Zbl0767.20014MR1096169
  4. [BK1] Bonk ( M. ), Kleiner ( B.). — Rigidity for quasi-Möbius group actions, J. Differential Geom. vol. 61, no. 1, p. 81-106 (2002). Zbl1044.37015
  5. [BK2] Bonk ( M. ), Kleiner ( B.). - Quasisymmetric parametrizations of two-dimensional metric spheres, Invent. Math.150, no. 1, p. 127-183 (2002). Zbl1037.53023MR1930885
  6. [BH] Bridson ( M.), Haefliger ( A.). — "Metric spaces of non-positive curvature", Grundlehren der Mathematischen Wissenschaften , Vol. 319, Springer-Verlag (1999). Zbl0988.53001MR1744486
  7. [B] Buyalo ( S. ). - Euclidean planes in 3-dimensional manifolds of nonpositive curvature, Mat. Zametki, 43, p. 103-114 (1988). Zbl0644.53035MR932905
  8. [CJ] Casson ( A. ), Jungreis ( D.). - Convergence groups and Seifert fibered 3-manifolds, Inventiones Math., 118, F. 3, p. 441-456 (1994). Zbl0840.57005MR1296353
  9. [Ca] Cannon ( J. ). — The combinatorial Riemann mapping theorem, Acta Mathematica, 173, p. 155-234 (1994). Zbl0832.30012MR1301392
  10. [CS] Cannon ( J. ), Swensen ( E.). - Recognizing constant curvature discrete groups in dimension 3, Trans. Amer. Math. Soc., 350, p. 809-849 (1998). Zbl0910.20024MR1458317
  11. [E] Eberlein ( P.). - Geodesic flow on certain manifolds without conjugate points, Transaction of AMS, 167, p. 151-170 (1972). Zbl0209.53304MR295387
  12. [Ga1] Gabai ( D. ). — Convergence groups are Fuchsian groups , Annals of Mathematics, 136, p. 447-510 (1992). Zbl0785.57004MR1189862
  13. [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). Zbl0964.57015MR1677889
  14. [Ga3] Gabai ( D.). — A geometric and topological rigidity of hyperbolic 3-manifolds, Journ. of AMS, 10, p 37-74 (1997). Zbl0870.57014MR1354958
  15. [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). Zbl0764.57003MR1130180
  16. [Gri] Grigorchuk ( R.). - Growth degrees of p-groups and torsion-free groups, Math. USSR, Sb., 54, p. 185-205 (1985). Zbl0583.20024
  17. [Gro1] Gromov ( M.). - Groups of polynomial growth and expanding maps, Publ. of IHES, 53, p. 53-73 (1981). Zbl0474.20018MR623534
  18. [Gro2] Gromov ( M.). - Hyperbolic groups, In: "Essays in Group Theory", Publications of MSRI, Vol. 8, p. 75-264 (1987). Zbl0634.20015MR919829
  19. [Gro3] Gromov ( M.). - Asymptotic invariants of infinite groups, in "Geometric Group Theory", Vol. 2; London Math. Society Lecture Notes, 182, Cambridge Univ. Press (1993). Zbl0841.20039MR1253544
  20. [He1] Hempel ( J.). — "3-manifolds", Annals of Math. Studies, Vol. 86, Princeton Univ. Press, (1976). Zbl0345.57001MR415619
  21. [He2] Hempel ( J.). — Residual finiteness for 3-manifolds . In: Annals of Math. Studies, Vol. 111, Princeton Univ. Press, p. 373-396 (1987). Zbl0772.57002MR895623
  22. [I] Imanishi ( H.). - On the theorem of Denjoy-Sacksteder for codimension one foliations without holonomy, J. Math. Kyoto Univ., 14, p. 607-634 (1974). Zbl0296.57006MR368028
  23. [K] Kapovich ( M. ). — "Hyperbolic Manifolds and Discrete Groups", Birkhäuser (2001). Zbl0958.57001MR1792613
  24. [KK1] Kapovich ( M. ) , Kleiner ( B.). — Geometry of quasi-planes , Preprint (2004). 
  25. [KK2] Kapovich ( M. ) , Kleiner ( B.). - Weak hyperbolization conjecture for 3-dimensional CAT(0) groups, Preprint (2004). 
  26. [KL] Kapovich ( M.), Leeb ( B.), Quasi-isometries preserve the geometric decomposition of Haken manifolds, Inventiones Math , vol. 128, p. 393-416 (1997). Zbl0866.20033MR1440310
  27. [KI] Kleiner ( B. ). — Private communication. 
  28. [L] Long ( D.). — Immersions and embeddings of totally geodesic surfaces , Bull. London Math. Soc., 19, p. 481-484 (1987). Zbl0596.57011MR898729
  29. [Mc] Mcmullen ( C.). - Iterations on Teichmüller space, Inventiones Math., 99, N 2, p. 425-454 (1989). Zbl0695.57012
  30. [M1] Mess ( G.). — The Seifert conjecture and groups which are coarse quasi- isometric to planes, Preprint (1990). 
  31. [M2] Mess ( G.). — Private communication. 
  32. [Mor] Morgan ( J.). - On Thurston's Uniformization Theorem for Three-Dimensional Manifolds, In: "Smith Conjecture", Acad. Press, p. 37-136 (1984). Zbl0599.57002MR758464
  33. [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). Zbl0661.57004MR942518
  34. [MS2] Morgan ( J.), Shalen ( P.). - Free actions of surface groups on R-trees, Topology, vol. 30, no. 2, p. 143-154 (1991). Zbl0726.57001MR1098910
  35. [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). Zbl0915.53020MR1619839
  36. [O] Otal ( J.-P. ). - Le théorème d'hyperbolisation pour les varietes fibrees de dimension trois, Astérisque, vol. 235 (1996). Zbl0855.57003
  37. [P1] Plante ( J. ). - Foliations with measure preserving holonomy , Annals of Math., 102 N 2, p. 327-361 (1975). Zbl0314.57018MR391125
  38. [P2] Plante ( J.) , Solvable groups acting on the real line, Transactions of AMS, 278, N 1 (1983). Zbl0569.57012MR697084
  39. [R] Rips ( E.). — Group actions on R-trees, in preparation. 
  40. [Sc] Schroeder ( V. ). - Codimension one tori in manifolds of nonpositive curvature, Geom. Dedicata, 33, p. 251-265 (1990). Zbl0698.53026MR1050413
  41. [Sch] Schwartz ( R.). — The quasi-isometry classification of hyperbolic lattices, Math. Publ. of IHES, Vol. 82, p. 133-168 (1995). Zbl0852.22010MR1383215
  42. [Sco] Scott ( P. ). - A new proof of the annulus and torus theorems , Amer. Journal of Math., 102, p. 241-277 (1980). Zbl0439.57004MR564473
  43. [T] Thurston ( W.). — Hyperbolic structures on 3-manifolds, I, Annals of Math., 124, p. 203-246 (1986). Zbl0668.57015MR855294
  44. [Tu] Tukia ( P. ). — Homeomorphic conjugates of fuchsian groups, J. Reine Angew. Math.391, p. 1-54 (1988). Zbl0644.30027MR961162
  45. [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). Zbl0552.20017MR751150

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.