Heegaard Floer homology gives a powerful invariant of closed 3-manifolds. It is always computable in the purely combinatorial sense, but usually computing it needs a very hard work. However, for certain graph 3-manifolds, its minus-flavored Heegaard Floer homology can be easily computed in terms of lattice homology, due to Nemethi. I plan to give the basic definitions and constructions of Heegaard Floer theory and lattice homology, as well as the isomorphism between those two objects.
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