Phantom components in Fukaya categories of exotic Del Pezzo manifolds
Phantom components in Fukaya categories of exotic Del Pezzo manifolds
Let be a symplectic manifold homeomorphic to a Del Pezzo surface, and let its Fukaya category be considered. A phantom orthogonal component is an orthogonal component of the Fukaya category that is phantom. The exotic Del Pezzo phantom conjecture. There exist exotic symplectic manifolds homeomorphic to Del Pezzo surfaces that can be distinguished by phantom orthogonal components in their Fukaya categories. This conjecture predicts that Fukaya categories can detect exotic symplectic structures invisible to the underlying homeomorphism type. The source gives no resolution.
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Primary source
Christian Böhning, Hans-Christian Graf von Bothmer, Ludmil Katzarkov and Pawel Sosna, “Determinantal Barlow surfaces and phantom categories”, arXiv:1210.0343 (2012).
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