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Discreteness of Flux Groups 被引量:1

Discreteness of Flux Groups
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摘要 Let (M, ω) be a closed symplectic 2n-dimensional manifold. Donaldson in his paper showed that there exist 2m-dimensional symplectie submanifolds (V^2m,ω) of (M,ω), 1 ≤m ≤ n - 1, with (m - 1)-equivalent inclusions. On the basis of this fact we obtain isomorphic relations between kernel of Lefschetz map of M and kernels of Lefschetz maps of Donaldson submanifolds V^2m, 2 ≤ m ≤ n - 1. Then, using this relation, we show that the flux group of M is discrete if the action of π1 (M) on π2(M) is trivial and there exists a retraction r : M→ V, where V is a 4-dimensional Donaldson submanifold. And, in the symplectically aspherical case, we investigate the flux groups of the manifolds. Let (M, ω) be a closed symplectic 2n-dimensional manifold. Donaldson in his paper showed that there exist 2m-dimensional symplectie submanifolds (V^2m,ω) of (M,ω), 1 ≤m ≤ n - 1, with (m - 1)-equivalent inclusions. On the basis of this fact we obtain isomorphic relations between kernel of Lefschetz map of M and kernels of Lefschetz maps of Donaldson submanifolds V^2m, 2 ≤ m ≤ n - 1. Then, using this relation, we show that the flux group of M is discrete if the action of π1 (M) on π2(M) is trivial and there exists a retraction r : M→ V, where V is a 4-dimensional Donaldson submanifold. And, in the symplectically aspherical case, we investigate the flux groups of the manifolds.
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2006年第1期115-122,共8页 数学学报(英文版)
关键词 Symplectic diffeomorphisms FLUX Symplectically aspherical manifold Donaldson submanifold Symplectic diffeomorphisms, Flux, Symplectically aspherical manifold, Donaldson submanifold
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  • 1McDuff, D., Salamon, D.: Introduction to symplectic topology, 2nd Edition, Oxford University Press,Oxford, 1998.
  • 2Donaldson, S. K.: Symplectic submanifolds and almost-complex geometry. Journal of Differential Geometry, 44, 666-705 (1996).
  • 3Gottlieb, D.: A certain subgroup of the fundamental group. Amer. J. Math., 87, 840-856 (1956).
  • 4Lalonde, F., McDuff, D., Porterovich, L.: On the Flux Conjectures. CRM Proceedings and Lecture Notes,15, 69-85 (1998).
  • 5Brown, K.; Cohomologv of groups. SDringer-Verlag. Berlin. 1993.
  • 6Rudyak, Y., Tralle A.: On Symplectic manifolds with aspherical symplectic form. preprint.
  • 7Banyaga, A.: Isomorphisms between classical diffeomorphism groups. CRM Proceedings and Lecture Notes,15, 1-15 (1998).
  • 8Bredon Glen, E.: Topology and Geometry, Graduate Texts in Mathematics, Vol. 139, Springer-Verlag,New York, Inc., 1993.
  • 9Calabi, E.I On the group of automorphisms of a symplectic manifold, Problems in Analysis (Symposium in honour of S. Bochner), Princeton Univ. Press, 1-26, 1970.
  • 10Cho, M. S., Cho, Y. SI: Symplectic surfaces in symplectic four-manifolds. Taiwan Residents Jour. of Math., 7(1),78-87 (2003).

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