Floer homology and surface decompositions

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; / .M 0 ; 0 / is a sutured manifold decomposition then SFH .M 0 ; 0 / is a direct summand of SFH .M; /. To prove the decomposition formula we give an algorithm that computes SFH .M; / from a balanced diagram defining .M; / that generalizes the algorithm of Sarkar and Wang.