A spectral sequence on lattice homology
Lattice homology is a combinatorial homology theory that can be computed from the plumbing tree of a plumbed three manifold. In the case of negative definite plumbing tree with at most one bad vertex, it is possible to show that the lattice homology is isomorphic to the Heegaard Floer homology of the three manifold associated to the tree. The main result of this paper is the extension of the isomorphism to any plumbing tree with at most two bad vertices. The key of the proof is the existence of a spectral sequence from the lattice homology of a plumbing tree to the Heegaard Floer homology of the related three manifold. The construction of the spectral sequence starts from the knot Floer homology of the link determined by the plumbing graph and using [\textit{C. Manolescu} and \textit{P. Ozsváth}, ``Heegaard Floer homology and integer surgeries on links'', preprint 2010, \url{arXiv:1011.1317}] goes to the Heegaard Floer homology of the three manifold.
scientific article