Symplectic fillability of tight contact structures on torus bundles

We study weak versus strong symplectic llability of some tight contact structures on torus bundles over the circle. In particular, we prove that almost all of these tight contact structures are weakly, but not strongly symplectically llable. For the 3{torus this theorem was established by Eliashberg. AMS Classication 53D35; 57M50, 57R65

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