Geometry & Topology
- Geom. Topol.
- Volume 14, Number 3 (2010), 1303-1354.
The sutured Floer homology polytope
In this paper, we extend the theory of sutured Floer homology developed by the author. We first prove an adjunction inequality and then define a polytope in that is spanned by the –structures which support nonzero Floer homology groups. If is a taut surface decomposition, then an affine map projects onto a face of ; moreover, if , then every face of can be obtained in this way for some surface decomposition. We show that if is reduced, horizontally prime and , then is maximal dimensional in . This implies that if , then has depth at most . Moreover, SFH acts as a complexity for balanced sutured manifolds. In particular, the rank of the top term of knot Floer homology bounds the topological complexity of the knot complement, in addition to simply detecting fibred knots.
Geom. Topol., Volume 14, Number 3 (2010), 1303-1354.
Received: 16 February 2010
Revised: 2 April 2010
Accepted: 3 May 2010
First available in Project Euclid: 20 December 2017
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Juhász, András. The sutured Floer homology polytope. Geom. Topol. 14 (2010), no. 3, 1303--1354. doi:10.2140/gt.2010.14.1303. https://projecteuclid.org/euclid.gt/1513732227