Contents Online
Mathematical Research Letters
Volume 6 (1999)
Number 6
$4$-manifolds with inequivalent symplectic forms and $3$-manifolds with inequivalent fibrations
Pages: 681 – 696
DOI: https://dx.doi.org/10.4310/MRL.1999.v6.n6.a8
Authors
Abstract
We exhibit a closed, simply connected 4-manifold $X$ carrying two symplectic structures whose first Chern classes in $H^2(X,\hbox{\fontsize{9}{8}$\mathbb Z$})$ lie in disjoint orbits of the diffeomorphism group of $X$. Consequently, the moduli space of symplectic forms on $X$ is disconnected. The example $X$ is in turn based on a 3-manifold $M$. The symplectic structures on $X$ come from a pair of fibrations $\pi_0, \pi_1 : M \arrow S^1$ whose Euler classes lie in disjoint orbits for the action of $\Diff(M)$ on $H_1(M,\hbox{\fontsize{9}{8}$\reals$})$. }
Published 1 January 1999