Symplectic geometry as a prerequisite for Heegaard Floer homology

Question

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.

Answer 1

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.