ON THE TOPOLOGY OF DIFFEOMORPHISMS OF SYMPLECTIC 4-MANIFOLDS

Title & Authors
ON THE TOPOLOGY OF DIFFEOMORPHISMS OF SYMPLECTIC 4-MANIFOLDS
Kim, Jin-Hong;

Abstract
For a closed symplectic 4-manifold X, let $\small{Diff_0}$(X) be the group of diffeomorphisms of X smoothly isotopic to the identity, and let Symp(X) be the subgroup of $\small{Diff_0}$(X) consisting of symplectic automorphisms. In this paper we show that for any finitely given collection of positive integers {$\small{n_1}$, $\small{n_2}$, $\small{\ldots}$, $\small{n_k}$} and any non-negative integer m, there exists a closed symplectic (or K$\small{\ddot{a}}$hler) 4-manifold X with $\small{b_2^+}$ (X) > m such that the homologies $\small{H_i}$ of the quotient space $\small{Diff_0}$(X)/Symp(X) over the rational coefficients are non-trivial for all odd degrees i = $\small{2n_1}$ - 1, $\small{\ldots}$, $\small{2n_k}$ - 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$\small{\acute{c}}$.
Keywords
Seiberg-Witten invariants;symplectic diffeomorphism;symplectic structures;
Language
English
Cited by
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