Abstract
We describe a contact analog of the symplectic cut construction [L]. As an application we show that the group of contactomorphisms for certain overtwisted contact structures on lens spaces contains countably many non-conjugate two tori.
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B. Aebischer, M. Borer, M. Kälin, Ch. Leuenberger and H. M. Reimann,Symplectic Geometry, Birkhäuser Verlag, Basel, 1994, xii+239 pp.
C. Albert,Le théorème de réduction de Marsden-Weinstein en géométrie cosymplectique et de contact, Journal of Geometry and Physics6 (1989), 627–649.
Y. Eliashberg,Classification of overtwisted contact structures on 3-manifolds, Inventiones Mathematicae98 (1989), 623–637.
Y. Eliashberg,Filling by holomorphic discs and its applications, inGeometry of Low-dimensional Manifolds, 2 (Durham, 1989), London Mathematical Society Lecture Notes Series151, Cambridge University Press, Cambridge, 1990, pp. 45–67.
Y. Eliashberg,Contact 3-manifolds twenty years since J. Martinet’s work, Annales de l’Institut Fourier92 (1992), 165–192.
Y. Eliashberg,Symplectic topology in the nineties, Differential Geometry and its Applications9 (1998), 59–88.
H. Geiges,Constructions of contact manifolds, Mathematical Proceedings of the Cambridge Philosophical Society121 (1997), 455–464.
R. Gompf,A new construction of symplectic manifolds, Annals of Mathematics (2)142 (1995), 527–595.
M. Gromov,Pseudoholomorphic curves in symplectic manifolds, Inventiones Mathematicae82 (1985), 307–347.
E. Lerman,Symplectic cuts, Mathematical Research Letters2 (1995), 247–258.
E. Lerman, E. Meinrenken, S. Tolman and C. Woodward,Nonabelian convexity by symplectic cuts, Topology37 (1998), 245–259.
R. Palais,On the existence of slices for actions of non-compact Lie groups, Annals of Mathematics73 (1961), 295–322.
P. Ševera,Contact reductions, mechanics and duality, math.DS/9903168, http://xxx.lanl.gov/abs/math.DS/9903168.
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Supported by the NSF grant DMS-980305.
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Lerman, E. Contact cuts. Isr. J. Math. 124, 77–92 (2001). https://doi.org/10.1007/BF02772608
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DOI: https://doi.org/10.1007/BF02772608