The wrapped Fukaya category of a Weinstein manifold is generated by the Lagrangian cocore discs

The wrapped Fukaya category of a Weinstein manifold is generated by the Lagrangian cocore discs

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Georgios Dimitroglou Rizell, Uppsala University
Fine Hall 322

In a joint work with B. Chantraine, P. Ghiggini, and R. Golovko we decompose any object in the wrapped Fukaya category as a twisted complex built from the cocores of the critical (i.e. half-dimensional) handles in a Weinstein handle decomposition. The main tools used are the Floer homology theories of exact Lagrangian immersions, of exact Lagrangian cobordisms in the SFT sense (i.e. between Legendrians), as well as relations between these theories. Note that exact Lagrangians admit Legendrian lifts, and that appropriate Lagrange surgeries can be seen to give rise to an exact Lagrangian cobordism of the aforementioned type.