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Journal of the Korean Mathematical Society = 대한수학회지 v.47 no.4, 2010년, pp.675 - 689   SCIE SCOPUS
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ON THE TOPOLOGY OF DIFFEOMORPHISMS OF SYMPLECTIC 4-MANIFOLDS

Kim, Jin-Hong    (DEPARTMENT OF MATHEMATICAL SCIENCES KOREA ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY  );
  • 초록

    For a closed symplectic 4-manifold X, let $Diff_0$ (X) be the group of diffeomorphisms of X smoothly isotopic to the identity, and let Symp(X) be the subgroup of $Diff_0$ (X) consisting of symplectic automorphisms. In this paper we show that for any finitely given collection of positive integers { $n_1$ , $n_2$ , $\ldots$ , $n_k$ } and any non-negative integer m, there exists a closed symplectic (or K $\ddot{a}$ hler) 4-manifold X with $b_2^+$ (X) > m such that the homologies $H_i$ of the quotient space $Diff_0$ (X)/Symp(X) over the rational coefficients are non-trivial for all odd degrees i = $2n_1$ - 1, $\ldots$ , $2n_k$ - 1. The basic idea of this paper is to use the local invariants for symplectic 4-manifolds with contact boundary, which are extended from the invariants of Kronheimer for closed symplectic 4-manifolds, as well as the symplectic compactifications of Stein surfaces of Lisca and Mati $\acute{c}$ .


  • 주제어

    Seiberg-Witten invariants .   symplectic diffeomorphism .   symplectic structures.  

  • 참고문헌 (25)

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