The wrapped Fukaya category of a Weinstein manifold is generated by the cocores of the critical handles

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• Paolo Ghiggini (CNRS (Centre national de la recherche scientifique); Université de Nantes)
• Thursday 09 March 2017, 15:15-16:15
• Seminar Room 2, Newton Institute.

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HTL - Homology theories in low dimensional topology

A Weinstein manifold is an open symplectic manifold admitting a handle decomposition adapted to the symplectic structure. It turns out that the handles of such a decomposition have index at most half of the dimension. When the index is half the dimension, they are called critical handles and their cocores are Lagrangian discs.

In a joint work with Baptiste Chantraine, Georgios Dimitroglou Rizell and Roman Golovko, we decompose any object in the wrapped Fukaya category of a Weinstein manifold as a twisted complex built from the cocores of the critical 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.

Since most participants of the HTL program are not experts in Fukaya categories (including me, actually) I will try to take it easy.

This talk is part of the Isaac Newton Institute Seminar Series series.

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