Quick note: “A symplectic prolegomenon”

I just want to draw your attention to a survey that appeared on the arXiv on January 1: A symplectic prolegomenon, by Ivan Smith.  The main point is to motivate and illustrate the Fukaya category, and to show how its algebraic structures amplify the power of Floer cohomology.  Smith uses the running examples of the nearby Lagrangian conjecture and the symplectic mapping class group to demonstrate these algebraic structures (the Oh spectral sequence, the exact triangle associated to a Dehn twist, …) in action.  There are lots of applications throughout, and one nice feature is that section 5 consists of explicit descriptions of the Fukaya categories of six (families of) symplectic manifolds.

So it’s great winter break reading, check it out!  It collects together a lot of information that had previously been scattered over a bunch of different papers.  And it includes the take-home messages of a number of rather intimidating papers.

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