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Journal of Modern Dynamics (JMD)
 

Contact homology of orbit complements and implied existence
Pages: 409 - 472, Issue 3, July 2011

doi:10.3934/jmd.2011.5.409      Abstract        References        Full text (841.1K)           Related Articles

Al Momin - Department of Mathematics, Purdue University, 150 N. University St. , West Lafayette, IN 47906, United States (email)

1 Sigurd B. Angenent, Curve shortening and the topology of closed geodesics on surfaces, Ann. of Math. (2), 162 (2005), 1187-1241.       
2 Frédéric Bourgeois, Kai Cieliebak and Tobias Ekholm, A note on Reeb dynamics on the tight 3-sphere, J. Mod. Dyn., 1 (2007), 597-613.       
3 F. Bourgeois, Y. Eliashberg, H. Hofer, K. Wysocki and E. Zehnder, Compactness results in symplectic field theory, Geom. Topol., 7 (2003), 799-888.       
4 Frédéric Bourgeois and Klaus Mohnke, Coherent orientations in symplectic field theory, Math. Z., 248 (2004), 123-146.       
5 Frédéric Bourgeois, "A Morse-Bott Approach to Contact Homology," Ph.D. thesis, Stanford University, 2002.       
6 Frédéric Bourgeois, Contact homology and homotopy groups of the space of contact structures, Math. Res. Lett., 13 (2006), 71-85.       
7 Andrew Cotton-Clay, Symplectic Floer homology of area-preserving surface diffeomorphisms, Geom. Topol., 13 (2009), 2619-2674.       
8 V. Colin, P. Ghiggini, K. Honda and M. Hutchings, Sutures and contact homology I, arXiv:1004.2942, 2010.
9 V. Colin and K. Honda, Reeb vector fields and open book decompositions, arXiv:0809.5088.
10 Vincent Colin and Ko Honda, Stabilizing the monodromy of an open book decomposition, Geom. Dedicata, 132 (2008), 95-103.       
11 Vincent Colin, Ko Honda and François Laudenbach, On the flux of pseudo-Anosov homeomorphisms, Algebr. Geom. Topol., 8 (2008), 2147-2160.       
12 J. C. Cha and C. Livingston, Knotinfo: Table of knot invariants. Available from: http://www.indiana.edu/~knotinfo.
13 Dragomir L. Dragnev, Fredholm theory and transversality for noncompact pseudoholomorphic maps in symplectizations, Comm. Pure Appl. Math., 57 (2004), 726-763.       
14 Y. Eliashberg, A. Givental and H. Hofer, Introduction to symplectic field theory, GAFA 2000 (Tel Aviv, 1999), in "Geom. Funct. Anal. 2000," Special Volume, Part II, 560-673.       
15 John B. Etnyre and Jeremy Van Horn-Morris, Fibered transverse knots and the Bennequin bound, International Mathematics Research Notices, 2011 (2011), 1483-1509.
16 Yakov Eliashberg, Sang Seon Kim and Leonid Polterovich, Geometry of contact transformations and domains: Orderability versus squeezing, Geom. Topol., 10 (2006), 1635-1747.       
17 Andreas Floer, Helmut Hofer and Dietmar Salamon, Transversality in elliptic Morse theory for the symplectic action, Duke Math. J., 80 (1995), 251-292.       
18 John Franks, Geodesics on $S^2$ and periodic points of annulus homeomorphisms, Invent. Math., 108 (1992), 403-418.       
19 David Gabai, Detecting fibred links in $S^3$, Comment. Math. Helv., 61 (1986), 519-555.       
20 Hansjörg Geiges, "An Introduction to Contact Topology," Cambridge Studies in Advanced Mathematics, 109, Cambridge University Press, Cambridge, 2008.       
21 E. Giroux, Géométrie de contact: De la dimension trois vers les dimensions supérieures, in "Proceedings of the International Congress of Mathematicians," Vol. II (Beijing, 2002), Higher Ed. Press, Beijing, (2002), 405-414.       
22 R. W. Ghrist, J. B. Van den Berg and R. C. Vandervorst, Morse theory on spaces of braids and Lagrangian dynamics, Invent. Math., 152 (2003), 369-432.       
23 R. W. Ghrist, J. B. Van den Berg, R. C. Vandervorst and W. Wójcik, Braid Floer homology, arXiv:0910.0647.
24 Matthew Hedden, An Ozsváth-Szabó Floer homology invariant of knots in a contact manifold, Adv. Math., 219 (2008), 89-117.       
25 Umberto Hryniewicz, Al Momin and Pedro Salomão, A Poincaré-Birkhoff Theorem for Reeb flows on $S^3$, preprint, arXiv:1110.3782.
26 Adam Harris and Gabriel P. Paternain, Dynamically convex Finsler metrics and $J$-holomorphic embedding of asymptotic cylinders, Ann. Global Anal. Geom., 34 (2008), 115-134.       
27 U. Hryniewicz and P. A. S. Salomão, On the existence of disk-like global sections for Reeb flows on the tight 3-sphere, to appear in Duke Mathematical Journal.
28 Michael Hutchings, An index inequality for embedded pseudoholomorphic curves in symplectizations, J. Eur. Math. Soc. (JEMS), 4 (2002), 313-361.       
29 H. Hofer, K. Wysocki and E. Zehnder, Properties of pseudo-holomorphic curves in symplectisations. II. Embedding controls and algebraic invariants, Geom. Funct. Anal., 5 (1995), 270-328.       
30 _____, Properties of pseudoholomorphic curves in symplectisations. I. Asymptotics, Ann. Inst. H. Poincaré Anal. Non Linéaire, 13 (1996), 337-379.       
31 _____, The dynamics on three-dimensional strictly convex energy surfaces, Ann. of Math. (2), 148 (1998), 197-289.       
32 _____, Finite energy foliations of tight three-spheres and Hamiltonian dynamics, Ann. of Math. (2), 157 (2003), 125-255.       
33 Helmut Hofer and Eduard Zehnder, "Symplectic Invariants and Hamiltonian Dynamics," Birkhäuser Advanced Texts: Basler Lehrbücher, [Birkhäuser Advanced Texts: Basel Textbooks], Birkhäuser Verlag, Basel, 1994.       
34 A. B. Katok, Ergodic perturbations of degenerate integrable Hamiltonian systems, Izv. Akad. Nauk SSSR Ser. Mat., 37 (1973), 539-576.       
35 Dusa McDuff, The local behaviour of holomorphic curves in almost complex 4-manifolds, J. Differential Geom., 34 (1991), 143-164.       
36 Mario J. Micallef and Brian White, The structure of branch points in minimal surfaces and in pseudoholomorphic curves, Ann. of Math. (2), 141 (1995), 35-85.       
37 Yi Ni, Knot Floer homology detects fibred knots, Invent. Math., 170 (2007), 577-608.       
38 Matthias Schwarz, "Cohomology Operations from $S^1$-Cobordisms in Floer Homology," Ph.D. thesis, ETH Zurich, 1995.
39 R. Siefring, Intersection theory of punctured pseudoholomorphic curves, to appear in Geometry & Topology, arXiv:0907.0470.
40 Richard Siefring, Relative asymptotic behavior of pseudoholomorphic half-cylinders, Comm. Pure Appl. Math., 61 (2008), 1631-1684.       
41 W. P. Thurston, Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle, arXiv:math/9801045, 1998.
42 W. P. Thurston and H. E. Winkelnkemper, On the existence of contact forms, Proc. Amer. Math. Soc., 52 (1975), 345-347.       
43 Chris Wendl, Automatic transversality and orbifolds of punctured holomorphic curves in dimension four, Comment. Math. Helv., 85 (2010), 347-407.       

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