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http://dx.doi.org/10.4134/JKMS.2010.47.4.675

ON THE TOPOLOGY OF DIFFEOMORPHISMS OF SYMPLECTIC 4-MANIFOLDS  

Kim, Jin-Hong (DEPARTMENT OF MATHEMATICAL SCIENCES KOREA ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY)
Publication Information
Journal of the Korean Mathematical Society / v.47, no.4, 2010 , pp. 675-689 More about this Journal
Abstract
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$\acute{c}$.
Keywords
Seiberg-Witten invariants; symplectic diffeomorphism; symplectic structures;
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