Abstract
Sutured Floer homology, denoted by , 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 is a sutured manifold decomposition then is a direct summand of . To prove the decomposition formula we give an algorithm that computes from a balanced diagram defining that generalizes the algorithm of Sarkar and Wang.
As a corollary we obtain that if is taut then . Other applications include simple proofs of a result of Ozsváth and Szabó that link Floer homology detects the Thurston norm, and a theorem of Ni that knot Floer homology detects fibred knots. Our proofs do not make use of any contact geometry.
Moreover, using these methods we show that if is a genus knot in a rational homology –sphere whose Alexander polynomial has leading coefficient and if then admits a depth taut foliation transversal to .
Citation
András Juhász. "Floer homology and surface decompositions." Geom. Topol. 12 (1) 299 - 350, 2008. https://doi.org/10.2140/gt.2008.12.299
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