A characterisation of the tight three-sphere
H. Hofer, K. Wysocki, and E. Zehnder
Source: Duke Math. J. Volume 81, Number 1
(1995), 159-226.
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Mathematical Reviews number (MathSciNet): MR1381975
Zentralblatt MATH identifier: 0861.57026
Digital Object Identifier: doi:10.1215/S0012-7094-95-08111-3
References
[1] C. Abbas and H. Hofer, Holomorphic Curves and Global Questions in Contact Geometry, Birkhäuser, Boston, to be published.
[2] D. Bennequin, Entrelacements et équations de Pfaff, Third Schnepfenried geometry conference, Vol. 1 (Schnepfenried, 1982), Astérisque, vol. 107, Soc. Math. France, Paris, 1983, pp. 87–161.
Mathematical Reviews (MathSciNet): MR86e:58070
Zentralblatt MATH: 0573.58022
[3] E. Bishop, Differentiable manifolds in complex Euclidean space, Duke Math. J. 32 (1965), 1–21.
Mathematical Reviews (MathSciNet): MR34:369
Zentralblatt MATH: 0154.08501
Digital Object Identifier: doi:10.1215/S0012-7094-65-03201-1
Project Euclid: euclid.dmj/1077375631
[4] J. Cerf, Sur les difféomorphismes de la sphère de dimension trois $(\Gamma \sb4=0)$, Lecture Notes in Mathematics, No. 53, Springer-Verlag, Berlin, 1968.
Mathematical Reviews (MathSciNet): MR37:4824
Zentralblatt MATH: 0164.24502
[5] C. Conley and E. Zehnder, Morse type index theory for flows and periodic solutions for Hamiltonian equations, Comm. Pure Appl. Math. 37 (1984), no. 2, 207–253.
Mathematical Reviews (MathSciNet): MR86b:58021
Zentralblatt MATH: 0559.58019
Digital Object Identifier: doi:10.1002/cpa.3160370204
[6] Y. Eliashberg, Classification of contact structures on $\bold R\sp 3$, Internat. Math. Res. Notices (1993), no. 3, 87–91.
Mathematical Reviews (MathSciNet): MR94j:53038
Zentralblatt MATH: 0784.53022
Digital Object Identifier: doi:10.1155/S107379289300008X
[7] Y. Eliashberg, Classification of overtwisted contact structures on three manifolds, Invent. Math. 98 (1989), no. 3, 623–637.
Mathematical Reviews (MathSciNet): MR90k:53064
Zentralblatt MATH: 0684.57012
Digital Object Identifier: doi:10.1007/BF01393840
[8] Y. Eliashberg, Contact $3$-manifolds twenty years since J. Martinet's work, Ann. Inst. Fourier (Grenoble) 42 (1992), no. 1-2, 165–192.
Mathematical Reviews (MathSciNet): MR93k:57029
Zentralblatt MATH: 0756.53017
[9] Y. Eliashberg, Filling by holomorphic discs and its applications, Geometry of Low-dimensional Manifolds, 2 (Durham, 1989), London Math. Soc. Lecture Note Ser., vol. 151, Cambridge Univ. Press, Cambridge, 1990, pp. 45–67.
Mathematical Reviews (MathSciNet): MR93g:53060
Zentralblatt MATH: 0731.53036
[10] Y. Eliashberg, Legendrian and transversal knots in tight contact $3$-manifolds, Topological Methods in Modern Mathematics (Stony Brook, NY, 1991) eds. L. Goldberg and A. Phillips, Publish or Perish, Houston, Tex., 1993, pp. 171–193.
Mathematical Reviews (MathSciNet): MR94e:57005
Zentralblatt MATH: 0809.53033
[11] Y. Eliashberg and H. Hofer, A Hamiltonian characterization of the three-ball, Differential Integral Equations 7 (1994), no. 5-6, 1303–1324.
Mathematical Reviews (MathSciNet): MR95c:53038
Zentralblatt MATH: 0803.58045
[12] A. Floer, An instanton-invariant for $3$-manifolds, Comm. Math. Phys. 118 (1988), no. 2, 215–240.
Mathematical Reviews (MathSciNet): MR89k:57028
Zentralblatt MATH: 0684.53027
Digital Object Identifier: doi:10.1007/BF01218578
Project Euclid: euclid.cmp/1104161987
[13] A. Floer, Morse theory for Lagrangian intersections, J. Differential Geom. 28 (1988), no. 3, 513–547.
Mathematical Reviews (MathSciNet): MR90f:58058
Zentralblatt MATH: 0674.57027
Project Euclid: euclid.jdg/1214442477
[14] A. Floer, Symplectic fixed points and holomorphic spheres, Comm. Math. Phys. 120 (1989), no. 4, 575–611.
Mathematical Reviews (MathSciNet): MR90e:58047
Zentralblatt MATH: 0755.58022
Digital Object Identifier: doi:10.1007/BF01260388
Project Euclid: euclid.cmp/1104177909
[15] A. Floer, The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math. 41 (1988), no. 6, 775–813.
Mathematical Reviews (MathSciNet): MR89g:58065
Zentralblatt MATH: 0633.53058
Digital Object Identifier: doi:10.1002/cpa.3160410603
[16] A. Floer, H. Hofer, and D. Salamon, Transversality in elliptic Morse theory for the symplectic action, Duke Math. J. 80 (1995), no. 1, 251–292.
Mathematical Reviews (MathSciNet): MR96h:58024
Zentralblatt MATH: 0846.58025
Digital Object Identifier: doi:10.1215/S0012-7094-95-08010-7
Project Euclid: euclid.dmj/1077245861
[17] J. Franks, Geodesics on $S^2$ and periodic points of annulus homeomorphisms, Invent. Math. 108 (1992), no. 2, 403–418.
Mathematical Reviews (MathSciNet): MR93f:58192
Zentralblatt MATH: 0766.53037
Digital Object Identifier: doi:10.1007/BF02100612
[18] E. Giroux, Convexité en topologie de contact, Comment. Math. Helv. 66 (1991), no. 4, 637–677.
Mathematical Reviews (MathSciNet): MR93b:57029
Zentralblatt MATH: 0766.53028
Digital Object Identifier: doi:10.1007/BF02566670
[19] M. Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), no. 2, 307–347.
Mathematical Reviews (MathSciNet): MR87j:53053
Zentralblatt MATH: 0592.53025
Digital Object Identifier: doi:10.1007/BF01388806
[20] H. Hofer, Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three, Invent. Math. 114 (1993), no. 3, 515–563.
Mathematical Reviews (MathSciNet): MR94j:58064
Zentralblatt MATH: 0797.58023
Digital Object Identifier: doi:10.1007/BF01232679
[21] H. Hofer and D. Salamon, Floer homology and Novikov rings, The Floer Memorial Volume, Progr. Math., vol. 133, Birkhäuser, Basel, 1995, pp. 483–524.
Mathematical Reviews (MathSciNet): MR97f:57032
Zentralblatt MATH: 0842.58029
[22] H. Hofer and C. Viterbo, The Weinstein conjecture in the presence of holomorphic spheres, Comm. Pure Appl. Math. 45 (1992), no. 5, 583–622.
Mathematical Reviews (MathSciNet): MR93h:58055
Zentralblatt MATH: 0773.58021
Digital Object Identifier: doi:10.1002/cpa.3160450504
[23] H. Hofer, K. Wysocki, and E. Zehnder, The dynamics on a strictly convex energy surface in $R^4$, preprint.
[24] H. Hofer, K. Wysocki, and E. Zehnder, Properties of pseudoholomorphic curves in symplectisations I: Asymptotics, to appear in Analyse Nonlinéaire, May 1996.
Mathematical Reviews (MathSciNet): MR1395676
Zentralblatt MATH: 0861.58018
[25] H. Hofer, K. Wysocki, and E. Zehnder, Properties of pseudoholomorphic curves in symplectisations II: Embedding controls and algebraic invariants, to appear in Geom. Funct. Anal. 5, 1995.
Mathematical Reviews (MathSciNet): MR1334869
Zentralblatt MATH: 0845.57027
Digital Object Identifier: doi:10.1007/BF01895669
[26] H. Hofer, K. Wysocki, and E. Zehnder, Properties of pseudoholomorphic curves in symplectisations III: Fredholm theory, preprint.
Mathematical Reviews (MathSciNet): MR1725579
Zentralblatt MATH: 0924.58003
[27] H. Hofer and E. Zehnder, Symplectic invariants and Hamiltonian dynamics, Birkhäuser Advanced Texts: Basler Lehrbücher. [Birkhäuser Advanced Texts: Basel Textbooks], Birkhäuser Verlag, Basel, 1994.
Mathematical Reviews (MathSciNet): MR96g:58001
Zentralblatt MATH: 0805.58003
[28] J. Martinet, Formes de contact sur les variétés de dimension $3$, Proceedings of Liverpool Singularities Symposium, II (1969/1970), Springer, Berlin, 1971, 142–163. Lecture Notes in Math., Vol. 209.
Mathematical Reviews (MathSciNet): MR50:3263
Zentralblatt MATH: 0215.23003
[29] D. McDuff, The local behaviour of holomorphic curves in almost complex $4$-manifolds, J. Differential Geom. 34 (1991), no. 1, 143–164.
Mathematical Reviews (MathSciNet): MR93e:53050
Zentralblatt MATH: 0736.53038
Project Euclid: euclid.jdg/1214446994
[30] D. McDuff and D. Salamon, Introduction to Symplectic Topology, Oxford University Press, Oxford, to be published.
Mathematical Reviews (MathSciNet): MR1698616
[31] D. McDuff and D. Salamon, $J$-Holomorphic Curves and Quantum Cohomology, University Lecture Series, vol. 6, Amer. Math. Soc., Providence, 1994.
Mathematical Reviews (MathSciNet): MR95g:58026
Zentralblatt MATH: 0809.53002
[32] M. Micallef and B. White, The structure of branch points in minimal surfaces and in pseudoholomorphic curves, Ann. of Math. (2) 141 (1995), no. 1, 35–85.
Mathematical Reviews (MathSciNet): MR96a:58063
Zentralblatt MATH: 0873.53038
Digital Object Identifier: doi:10.2307/2118627
JSTOR: links.jstor.org
[33] Y. G. Oh, Removal of boundary singularities of pseudo-holomorphic curves with Lagrangian boundary conditions, Comm. Pure Appl. Math. 45 (1992), no. 1, 121–139.
Mathematical Reviews (MathSciNet): MR92k:58065
Zentralblatt MATH: 0743.58018
Digital Object Identifier: doi:10.1002/cpa.3160450106
[34] T. H. Parker and J. G. Wolfson, Pseudo-holomorphic maps and bubble trees, preprint, 1991.
Mathematical Reviews (MathSciNet): MR1197017
Zentralblatt MATH: 0759.53023
[35] J. Robbin and D. Salamon, The spectral flow and the Maslov index, to appear in J. London Math. Soc.
Mathematical Reviews (MathSciNet): MR1331677
Zentralblatt MATH: 0859.58025
Digital Object Identifier: doi:10.1112/blms/27.1.1
[36] D. Rohlfson, Knots, Publish or Perish, Houston, Tex., 1976.
[37] S. Smale, Diffeomorphisms of the $2$-sphere, Proc. Amer. Math. Soc. 10 (1959), 621–626.
Mathematical Reviews (MathSciNet): MR22:3004
Zentralblatt MATH: 0118.39103
Digital Object Identifier: doi:10.2307/2033664
JSTOR: links.jstor.org
[38] R. Ye, Filling by holomorphic disks in symplectic $4$-manifolds, preprint.
[39] R. Ye, Gromov's compactness theorem for pseudo holomorphic curves, Trans. Amer. Math. Soc. 342 (1994), no. 2, 671–694.
Mathematical Reviews (MathSciNet): MR94f:58030
Zentralblatt MATH: 0810.53024
Digital Object Identifier: doi:10.2307/2154647
JSTOR: links.jstor.org
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