Abstract:
The rational blowdown of $ M \ to M _ {(p)} $ is the rearrangement of a smooth
4-dimensional manifold that preserves the symplectic structure. By results of
Fintushel and Stern we know when the sequence of blow-ups, rearrangements
along links, and rational contractions leads to a manifold homeomorphic but
not diffeomorphic to the given one. By this construction many exotic symplectic
manifolds can be obtained, the geometry of which is not well-studied. In this work
we compute the Fukaya category $ M _ {(p)} $ by the Fukaya category $M$.
We prove an analogous result for symplectic homologies using the results of Ganatra.
|
