I would like to study Heegaard Floer homology in the future in the connection to knot theory.

I read a wikipedia article and it seems that I need to first learn a symplectic geometry (topology?). I took a basic differential geometry class. But I have never studied symplectic geometry.

What is a good way to study symplectic geometry in the scope of studying Heegaard Floer homology in the future? What textbook is adequate fo this purpose.

Also, what are the other prerequisites?

I know basics of algebraic topology.

  • 1
    $\begingroup$ I was briefly considering studying this, and I was told that McDuff--Salamon's "Intro to Symplectic Manifolds" is standard and that Ana Cannas da Silva's book is harder and contains lots of important stuff. $\endgroup$ – Aaron Mazel-Gee Apr 10 '13 at 6:28
  • $\begingroup$ Do you have someone in your department who can give you some guidance? there is a lot of symplectic geometry in both of these books that is not relevant to you and there are a number of technical points about holomorphic curves that are not explained in these books. A correct answer to your question, imo, requires more information about what you know and about what you are interested in doing. Unfortunately, even with this information, I wouldn't be qualified to give you a good answer, since I don't work in Heegaard Floer homology. $\endgroup$ – Sam Lisi Apr 11 '13 at 9:53

I recommend this book by Ana Cannas da Silva to learn about symplectic geometry.

However, if your primary interest is Heegaard Floer Knot homology, you can dive right in, using the combinatorial description of Ciprian Manolescu, Peter Ozsváth, Zoltán Szabó, and Dylan Thurston and begin calculating. Then, later approach it from the geometry of holomorphic disks.


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