# Floer homology and surface decompositions

@article{Juhsz2008FloerHA, title={Floer homology and surface decompositions}, author={Andr{\'a}s Juh{\'a}sz}, journal={Geometry \& Topology}, year={2008}, volume={12}, pages={299-350} }

Sutured Floer homology, denoted by SFH, is an invariant of balanced sutured manifolds previously defined by the author. In this paper we give a formula that shows how this invariant changes under surface decompositions. In particular, if (M, \gamma)--> (M', \gamma') is a sutured manifold decomposition then SFH(M',\gamma') is a direct summand of SFH(M, \gamma). To prove the decomposition formula we give an algorithm that computes SFH(M,\gamma) from a balanced diagram defining (M,\gamma) that… Expand

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