# 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}
}
• A. Juhász
• Published 28 September 2006
• Mathematics
• Geometry & Topology
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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