메뉴 건너뛰기




Volumn 19, Issue 4, 2009, Pages 1195-1228

Heegaard splittings and pseudo-Anosov maps

Author keywords

Geometrization; Heegaard splitting; Hyperbolic 3 manifolds; Rank conjecture

Indexed keywords


EID: 71049187571     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-009-0025-3     Document Type: Article
Times cited : (29)

References (44)
  • 3
    • 84972583778 scopus 로고
    • Degenerations of the hyperbolic space
    • Bestvina M.: Degenerations of the hyperbolic space. Duke Math. J. 56, 143-161 (1988).
    • (1988) Duke Math. J. , vol.56 , pp. 143-161
    • Bestvina, M.1
  • 4
    • 0000971510 scopus 로고
    • Cobordism of automorphisms of surfaces, Ann
    • Bonahon F.: Cobordism of automorphisms of surfaces, Ann. Sci. Ec. Norm. Super. IV Ser. 16, 237-270 (1983).
    • (1983) Sci. Ec. Norm. Super. IV Ser. , vol.16 , pp. 237-270
    • Bonahon, F.1
  • 5
    • 0002437863 scopus 로고
    • Bouts des variété hyperboliques de dimension 3
    • Bonahon F.: Bouts des variété hyperboliques de dimension 3. Ann. of Math. 124, 71-158 (1986).
    • (1986) Ann. Of Math. , vol.124 , pp. 71-158
    • Bonahon, F.1
  • 6
    • 0034366797 scopus 로고    scopus 로고
    • Continuity of Thurston's length function
    • Brock J.: Continuity of Thurston's length function. Geom. Funct. Anal. 10, 741-797 (2000).
    • (2000) Geom. Funct. Anal. , vol.10 , pp. 741-797
    • Brock, J.1
  • 7
    • 71049193534 scopus 로고    scopus 로고
    • D. Calegari, D. Gabai, Shrinkwrapping and the taming of hyperbolic 3-manifolds, preprint (2004)
    • D. Calegari, D. Gabai, Shrinkwrapping and the taming of hyperbolic 3-manifolds, preprint (2004).
  • 8
    • 84968484274 scopus 로고
    • Ends of hyperbolic 3-manifolds
    • Canary R. D.: Ends of hyperbolic 3-manifolds. J. Amer. Math. Soc. 6, 1-35 (1993).
    • (1993) J. Amer. Math. Soc. , vol.6 , pp. 1-35
    • Canary, R.D.1
  • 9
    • 0030186893 scopus 로고    scopus 로고
    • A covering theorem for hyperbolic 3-manifolds and its applications
    • Canary R. D.: A covering theorem for hyperbolic 3-manifolds and its applications. Topology 35, 751-778 (1996).
    • (1996) Topology , vol.35 , pp. 751-778
    • Canary, R.D.1
  • 10
    • 71049132783 scopus 로고    scopus 로고
    • R. D. Canary, D. B. A. Epstein, P. Green, Notes on notes of Thurston, in "Analytical and geometric aspects of hyperbolic space", London Math. Soc. Lecture Note Ser. 111, Cambridge University Press (1987), 3-92
    • R. D. Canary, D. B. A. Epstein, P. Green, Notes on notes of Thurston, in "Analytical and geometric aspects of hyperbolic space", London Math. Soc. Lecture Note Ser. 111, Cambridge University Press (1987), 3-92.
  • 11
    • 0001183919 scopus 로고
    • Reducing Heegaard splittings
    • Casson A., Gordon C.: Reducing Heegaard splittings. Topology Appl. 27, 275-283 (1987).
    • (1987) Topology Appl. , vol.27 , pp. 275-283
    • Casson, A.1    Gordon, C.2
  • 12
    • 0000755701 scopus 로고
    • The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature
    • Choi H. I., Schoen R.: The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature. Invent. Math. 81, 387-394 (1985).
    • (1985) Invent. Math. , vol.81 , pp. 387-394
    • Choi, H.I.1    Schoen, R.2
  • 13
    • 33646430037 scopus 로고    scopus 로고
    • Surface subgroups and handlebody attachments
    • (electronic)
    • Easson V. R.: Surface subgroups and handlebody attachments. Geom. Topol. 10, 557-591 (2006) (electronic).
    • (2006) Geom. Topol. , vol.10 , pp. 557-591
    • Easson, V.R.1
  • 14
    • 0036347429 scopus 로고    scopus 로고
    • Heegaard splittings of Haken manifolds have bounded distance
    • Hartshorn K.: Heegaard splittings of Haken manifolds have bounded distance. Pacific J. Math. 204, 61-75 (2002).
    • (2002) Pacific J. Math. , vol.204 , pp. 61-75
    • Hartshorn, K.1
  • 15
    • 71049125375 scopus 로고    scopus 로고
    • J. Hass, A. Thompson, W. Thurston, Stabilization of Heegaard splittings, preprint; arXiv: 0802. 2145
    • J. Hass, A. Thompson, W. Thurston, Stabilization of Heegaard splittings, preprint; arXiv: 0802. 2145.
  • 16
    • 0035343955 scopus 로고    scopus 로고
    • 3-manifolds as viewed from the curve complex
    • Hempel J.: 3-manifolds as viewed from the curve complex. Topology 40, 631-657 (2001).
    • (2001) Topology , vol.40 , pp. 631-657
    • Hempel, J.1
  • 17
    • 38249019947 scopus 로고
    • The measure of the limit set of the handlebody group
    • Kerckhoff S.: The measure of the limit set of the handlebody group. Topology 29, 27-40 (1990).
    • (1990) Topology , vol.29 , pp. 27-40
    • Kerckhoff, S.1
  • 18
    • 0036444097 scopus 로고    scopus 로고
    • Algebraic convergence of function groups
    • Kleineidam G., Souto J.: Algebraic convergence of function groups. Comment. Math. Helv. 77, 244-269 (2002).
    • (2002) Comment. Math. Helv. , vol.77 , pp. 244-269
    • Kleineidam, G.1    Souto, J.2
  • 19
    • 71049141387 scopus 로고    scopus 로고
    • G. Kleineidam, J. Souto, Ending laminations in theMasur domain, in "Kleinian Groups and Hyperbolic 3-Manifolds," Poceeddings of Warwick Conference 2001, London Math. Soc. (2003), 105-129
    • G. Kleineidam, J. Souto, Ending laminations in theMasur domain, in "Kleinian Groups and Hyperbolic 3-Manifolds," Poceeddings of Warwick Conference 2001, London Math. Soc. (2003), 105-129.
  • 20
    • 4243098379 scopus 로고    scopus 로고
    • Attaching handlebodies to 3-manifolds
    • Lackenby M.: Attaching handlebodies to 3-manifolds. Geom. Topol. 6, 889-904 (2002).
    • (2002) Geom. Topol. , vol.6 , pp. 889-904
    • Lackenby, M.1
  • 21
    • 33645508714 scopus 로고    scopus 로고
    • Heegaard splittings, the virtually Haken conjecture and Property τ
    • Lackenby M.: Heegaard splittings, the virtually Haken conjecture and Property τ. Invent. Math. 164, 317-359 (2006).
    • (2006) Invent. Math. , vol.164 , pp. 317-359
    • Lackenby, M.1
  • 22
    • 0002223191 scopus 로고
    • Measured foliations and handlebodies
    • Masur H. A.: Measured foliations and handlebodies. Ergodic Theory Dynam. Systems 6, 99-116 (1986).
    • (1986) Ergodic Theory Dynam. Systems , vol.6 , pp. 99-116
    • Masur, H.A.1
  • 23
    • 71049194895 scopus 로고    scopus 로고
    • K. Matsuzaki, M. Taniguchi, Hyperbolic Manifolds and Kleinian Groups, Oxford Mathematical Monographs. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, (1998)
    • K. Matsuzaki, M. Taniguchi, Hyperbolic Manifolds and Kleinian Groups, Oxford Mathematical Monographs. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, (1998).
  • 25
    • 0035637007 scopus 로고    scopus 로고
    • Bounded geometry for Kleinian groups
    • Minsky Y. N.: Bounded geometry for Kleinian groups. Invent. Math. 146, 143-192 (2001).
    • (2001) Invent. Math. , vol.146 , pp. 143-192
    • Minsky, Y.N.1
  • 26
    • 71049116886 scopus 로고    scopus 로고
    • H. Namazi, Heegaard splittings and hyperbolic geometry, Dissertation Research, Stony Brook University, 2005
    • H. Namazi, Heegaard splittings and hyperbolic geometry, Dissertation Research, Stony Brook University, 2005.
  • 27
    • 71049181919 scopus 로고    scopus 로고
    • J.-P. Otal, Courants géodésiques et produits libres, Thése d'Etat, Université Paris-Sud, Orsay, 1988
    • J.-P. Otal, Courants géodésiques et produits libres, Thése d'Etat, Université Paris-Sud, Orsay, 1988.
  • 28
    • 84973997572 scopus 로고
    • Sur la dégénerescence des groupes de Schottky
    • Otal J.-P.: Sur la dégénerescence des groupes de Schottky. Duke Math. J. 74, 777-792 (1994).
    • (1994) Duke Math. J. , vol.74 , pp. 777-792
    • Otal, J.-P.1
  • 29
    • 71049188169 scopus 로고    scopus 로고
    • J.-P. Otal, Théor'eme d'hyperbolisation pour les variété fibrées de dimension 3, Astérisque, Société Mathématique de France, (1996)
    • J.-P. Otal, Théor'eme d'hyperbolisation pour les variété fibrées de dimension 3, Astérisque, Société Mathématique de France, (1996).
  • 30
    • 0002832883 scopus 로고
    • Topologie de Gromov équivariante, structures hyperboliques et arbres réels
    • Paulin F.: Topologie de Gromov équivariante, structures hyperboliques et arbres réels. Invent. Math. 94, 53-80 (1988).
    • (1988) Invent. Math. , vol.94 , pp. 53-80
    • Paulin, F.1
  • 31
    • 71049194471 scopus 로고    scopus 로고
    • J. Pérez, A. Ros, Properly embedded minimal surfaces with finite total curvature, in "The global theory of minimal surfaces in flat spaces", Springer Lecture Notes in Math. 1775 (2002), 15-66
    • J. Pérez, A. Ros, Properly embedded minimal surfaces with finite total curvature, in "The global theory of minimal surfaces in flat spaces", Springer Lecture Notes in Math. 1775 (2002), 15-66.
  • 32
    • 0000952296 scopus 로고
    • Minimal immersions of closed riemann surfaces
    • Sacks J., Uhlenbeck K.: Minimal immersions of closed riemann surfaces. Trans. Amer. Math. Soc. 271, 639-652 (1982).
    • (1982) Trans. Amer. Math. Soc. , vol.271 , pp. 639-652
    • Sacks, J.1    Uhlenbeck, K.2
  • 33
    • 33646423548 scopus 로고    scopus 로고
    • Alternate Heegaard genus bounds distance
    • (electronic)
    • Scharlemann M., Tomova M.: Alternate Heegaard genus bounds distance. Geom. Topol. 10, 593-617 (2006) (electronic).
    • (2006) Geom. Topol. , vol.10 , pp. 593-617
    • Scharlemann, M.1    Tomova, M.2
  • 34
    • 0001593830 scopus 로고
    • Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature
    • Schoen R., Yau S. T.: Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature. Annals of Math. 110, 127-142 (1979).
    • (1979) Annals of Math. , vol.110 , pp. 127-142
    • Schoen, R.1    Yau, S.T.2
  • 35
    • 84959841963 scopus 로고    scopus 로고
    • P. Scott, Compact submanifolds of 3-manifolds, Journal London Math. Soc. 7 (1973)
    • P. Scott, Compact submanifolds of 3-manifolds, Journal London Math. Soc. 7 (1973).
  • 36
    • 84968468173 scopus 로고
    • Splittings of surfaces
    • Skora R.: Splittings of surfaces. Bull. Amer. Math. Soc. 23, 85-90 (1990).
    • (1990) Bull. Amer. Math. Soc. , vol.23 , pp. 85-90
    • Skora, R.1
  • 37
    • 0030529002 scopus 로고    scopus 로고
    • Splittings of surfaces
    • Skora R.: Splittings of surfaces. J. Amer. Math. Soc. 9, 605-616 (1996).
    • (1996) J. Amer. Math. Soc. , vol.9 , pp. 605-616
    • Skora, R.1
  • 38
    • 71049168048 scopus 로고    scopus 로고
    • J. Souto, The rank of the fundamental group of hyperbolic 3-manifolds fibering over the circle, in "The Zieschang Gedenkschrift", Geometry and Topology Monographs 14 (2008)
    • J. Souto, The rank of the fundamental group of hyperbolic 3-manifolds fibering over the circle, in "The Zieschang Gedenkschrift", Geometry and Topology Monographs 14 (2008).
  • 39
    • 71049156335 scopus 로고    scopus 로고
    • J. Souto, Geometry of Heegaard splittings, in preparation
    • J. Souto, Geometry of Heegaard splittings, in preparation.
  • 40
    • 0001182097 scopus 로고
    • Hyperbolic structures on 3-manifolds I: Deformation of acylindrical manifolds
    • Thurston W. P.: Hyperbolic structures on 3-manifolds I: Deformation of acylindrical manifolds. Annals of Math. 124, 203-246 (1986).
    • (1986) Annals of Math. , vol.124 , pp. 203-246
    • Thurston, W.P.1
  • 41
    • 71049125374 scopus 로고    scopus 로고
    • W. P. Thurston, Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over he circle, preprint; math. GT/9801045
    • W. P. Thurston, Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over he circle, preprint; math. GT/9801045.
  • 42
    • 71049185203 scopus 로고    scopus 로고
    • G. Tian, A pinching theorem on manifolds with negative curvature, Proceedings of International Conference on Algebraic and Analytic Geometry, Tokyo (1990)
    • G. Tian, A pinching theorem on manifolds with negative curvature, Proceedings of International Conference on Algebraic and Analytic Geometry, Tokyo (1990).
  • 43
    • 0000250701 scopus 로고
    • Heegaard-Zerlegungen der 3-Sphäre
    • Waldhausen F.: Heegaard-Zerlegungen der 3-Sphäre. Topology 7, 195-203 (1968).
    • (1968) Topology , vol.7 , pp. 195-203
    • Waldhausen, F.1
  • 44
    • 0042349423 scopus 로고    scopus 로고
    • Injectivity radius and fundamental groups of hyperbolic 3-manifolds
    • White M.: Injectivity radius and fundamental groups of hyperbolic 3-manifolds. Comm. Anal. Geom. 10, 377-395 (2002).
    • (2002) Comm. Anal. Geom. , vol.10 , pp. 377-395
    • White, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.