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Title:
An A-infinity functor and a refined super potential associated
to a Weinstein skeleton.
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Abstract:
The skeleton of a Weinstein manifold can be seen as a Lagrangian with conical singularities. Using this singular Lagrangian we associate a geometrically defined A-infinity functor from the compact Fukaya category to the category of modules over the wrapped Fukaya category. In the monotone case, one can associate a refined super potential and, moreover, one obtains a functor to an associated matrix factorisation category. In joint work with Ghiggini we develop this theory and apply it to the case of a singular Lagrangian in CP^n that corresponds to a local SYZ singularity. The particular case of the Whitney immersion in CP^2, which also will be discussed, was considered in joint work with Ekholm-Tonkonog.
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