Abstract
We define symplectic fractional twists, which subsume Dehn twists and fibered twists and use these in open books to investigate contact structures. The resulting contact structures are invariant under a circle action, and share several similarities with the invariant contact structures that were studied by Lutz and Giroux. We show that left-handed fractional twists often give rise to “algebraically overtwisted” contact manifolds, a certain class of non-fillable contact manifolds.
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