Geometry & Topology Volume 10, issue 3 (2006)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Geometry of contact transformations and domains: orderability versus squeezing

Yakov Eliashberg, Sang Seon Kim and Leonid Polterovich

Geometry & Topology 10 (2006) 1635–1747

DOI: 10.2140/gt.2006.10.1635

Bibliography

1	A Abbondandolo, M Schwarz, On the Floer homology of cotangent bundles, Comm. Pure Appl. Math. 59 (2006) 254 MR2190223
2	G Baumslag, A G Myasnikov, V Shpilrain, Open problems in combinatorial group theory. Second edition, from: "Combinatorial and geometric group theory (New York, 2000/Hoboken, NJ, 2001)", Contemp. Math. 296, Amer. Math. Soc. (2002) 1 MR1921705
3	P Biran, L Polterovich, D Salamon, Propagation in Hamiltonian dynamics and relative symplectic homology, Duke Math. J. 119 (2003) 65 MR1991647
4	F Bourgeois, A Morse–Bott approach to contact homology, from: "Symplectic and contact topology: interactions and perspectives (Toronto, ON/Montreal, QC, 2001)" (editors Y Elashberg, B Khesin, F Lalonde), Fields Inst. Commun. 35, Amer. Math. Soc. (2003) 55 MR1969267
5	F Bourgeois, Contact homology and homotopy groups of the space of contact structures, Math. Res. Lett. 13 (2006) 71 MR2200047
6	F Bourgeois, Y Eliashberg, H Hofer, K Wysocki, E Zehnder, Compactness results in symplectic field theory, Geom. Topol. 7 (2003) 799 MR2026549
7	E M Chirka, Complex analytic sets, Mathematics and its Applications (Soviet Series) 46, Kluwer Academic Publishers Group (1989) MR1111477
8	K Cieliebak, Subcritical manifolds are split arXiv:math.DG/0204351
9	K Cieliebak, A Floer, H Hofer, Symplectic homology II: A general construction, Math. Z. 218 (1995) 103 MR1312580
10	K Cieliebak, V L Ginzburg, E Kerman, Symplectic homology and periodic orbits near symplectic submanifolds, Comment. Math. Helv. 79 (2004) 554 MR2081726
11	K Cieliebak, H Hofer, J Latschev, F Schlenk, Quantitative symplectic geometry arXiv:math.SG/0506191
12	M de Gosson, The symplectic camel and phase space quantization, J. Phys. A 34 (2001) 10085 MR1872403
13	M de Gosson, Phase space quantization and the uncertainty principle, Phys. Lett. A 317 (2003) 365 MR2027474
14	D L Dragnev, Fredholm theory and transversality for noncompact pseudoholomorphic maps in symplectizations, Comm. Pure Appl. Math. 57 (2004) 726 MR2038115
15	Y Eliashberg, Topological characterization of Stein manifolds of dimension $\gt 2$, Internat. J. Math. 1 (1990) 29 MR1044658
16	Y Eliashberg, New invariants of open symplectic and contact manifolds, J. Amer. Math. Soc. 4 (1991) 513 MR1102580
17	Y Eliashberg, A Givental, H Hofer, Introduction to symplectic field theory, GAFA 2000 $($Tel Aviv, 1999$)$, Geom. Funct. Anal. (2000) 560 MR1826267
18	Y Eliashberg, M Gromov, Convex symplectic manifolds, from: "Several complex variables and complex geometry, Part 2 (Santa Cruz, CA, 1989)", Proc. Sympos. Pure Math. 52, Amer. Math. Soc. (1991) 135 MR1128541
19	Y Eliashberg, L Polterovich, Partially ordered groups and geometry of contact transformations, Geom. Funct. Anal. 10 (2000) 1448 MR1810748
20	Y Félix, J C Thomas, M Vigué-Poirrier, Free loop spaces of finite complexes have infinite category, Proc. Amer. Math. Soc. 111 (1991) 869 MR1025277
21	A Floer, Symplectic fixed points and holomorphic spheres, Comm. Math. Phys. 120 (1989) 575 MR987770
22	A Floer, H Hofer, Symplectic homology I: Open sets in $\mathbf{C}^n$, Math. Z. 215 (1994) 37 MR1254813
23	A Floer, H Hofer, K Wysocki, Applications of symplectic homology I, Math. Z. 217 (1994) 577 MR1306027
24	H Geiges, Contact geometry, from: "Handbook of differential geometry. Vol. II", Elsevier/North-Holland, Amsterdam (2006) 315 MR2194671
25	V L Ginzburg, B Z Gürel, Relative Hofer–Zehnder capacity and periodic orbits in twisted cotangent bundles, Duke Math. J. 123 (2004) 1 MR2060021
26	E Giroux, Convexité en topologie de contact, Comment. Math. Helv. 66 (1991) 637 MR1129802
27	A Givental, Nonlinear generalization of the Maslov index, from: "Theory of singularities and its applications", Adv. Soviet Math. 1, Amer. Math. Soc. (1990) 71 MR1089671
28	M Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
29	J Hilgert, K H Neeb, Lie semigroups and their applications, Lecture Notes in Mathematics 1552, Springer (1993) MR1317811
30	J Hilgert, G Ólafsson, Causal symmetric spaces, Geometry and harmonic analysis, Perspectives in Mathematics 18, Academic Press (1997) MR1407033
31	H Hofer, K Wysocki, E Zehnder, Properties of pseudoholomorphic curves in symplectizations. III. Fredholm theory, from: "Topics in nonlinear analysis", Progr. Nonlinear Differential Equations Appl. 35, Birkhäuser (1999) 381 MR1725579
32	H Hofer, E Zehnder, Symplectic invariants and Hamiltonian dynamics, Birkhäuser Advanced Texts, Birkhäuser (1994) MR1306732
33	S Jackowski, J Słomińska, $G$–functors, $G$–posets and homotopy decompositions of $G$–spaces, Fund. Math. 169 (2001) 249 MR1852128
34	F Lalonde, D McDuff, The geometry of symplectic energy, Ann. of Math. $(2)$ 141 (1995) 349 MR1324138
35	F Lalonde, D McDuff, Hofer's $L^\infty$–geometry: energy and stability of Hamiltonian flows I, II, Invent. Math. 122 (1995) 1, 35 MR1354953
36	J A Makowsky, On some conjectures connected with complete sentences, from: "Collection of articles dedicated to Andrzej Mostowski on the occasion of his sixtieth birthday, III", Fund. Math. 81 (1974) 193 MR0366647
37	D McDuff, D Salamon, $J$–holomorphic curves and symplectic topology, American Mathematical Society Colloquium Publications 52, American Mathematical Society (2004) MR2045629
38	M J Micallef, B White, The structure of branch points in minimal surfaces and in pseudoholomorphic curves, Ann. of Math. $(2)$ 141 (1995) 35 MR1314031
39	G I Olshanskii, Invariant orderings in simple Lie groups. Solution of a problem of E. B Vinberg, Funktsional. Anal. i Prilozhen. 16 (1982) MR684139
40	J Palis Jr., W de Melo, Geometric theory of dynamical systems, Springer (1982) MR669541
41	J Robbin, D Salamon, The Maslov index for paths, Topology 32 (1993) 827 MR1241874
42	W Rudin, Function theory in the unit ball of $\mathbf{C}^{n}$, Grundlehren series 241, Springer (1980) MR601594
43	D Salamon, J Weber, Floer homology and the heat flow, Geom. Funct. Anal. $($GAFA$)$. to appear arXiv:math.SG/0304383
44	I Ustilovsky, Infinitely many contact structures on $S^{4m+1}$, Internat. Math. Res. Notices (1999) 781 MR1704176
45	C Viterbo, Functors and computations in Floer homology with applications, Part II
46	C Viterbo, Metric and isoperimetric problems in symplectic geometry, J. Amer. Math. Soc. 13 (2000) 411 MR1750956
47	J Weber, Noncontractible periodic orbits in cotangent bundles and Floer homology, Duke Math. J. 133 (2006) 527 MR2228462
48	M L Yau, Cylindrical contact homology of subcritical Stein-fillable contact manifolds, Geom. Topol. 8 (2004) 1243 MR2087083