The sutured Floer homology polytope

By Andr'as Juh'asz. 2008

63 citations recorded by the source corpus.

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 P(M,g) in H^2(M,\partial M; R) that is spanned by the Spin^c-structures which support non-zero Floer homology groups. If (M,g) --> (M',g') is a taut surface decomposition, then a natural map projects P(M',g') onto a face of P(M,g); moreover, if H_2(M) = 0, then every face of P(M,g) can be obtained in this way for some surface decomposition. We show that if (M,g) is reduced, horizontally prime, and H_2(M) = 0, then P(M,g) is maximal dimensional in H^2(M,\partial M; R). This implies that if rk(SFH(M,g)) < 2^{k+1} then (M,g) has depth at most 2k. 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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e03bee3229e0bbb407c2e8ee153d45fb67d29b0e

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Citations in the corpus

The decategorification of sutured Floer homology (2009, methodology): “For all the necessary definitions, also see [17].”
Knots, sutures, and excision (2008, background): “Juhász [14] has considered an extension of the fibering theorem, which prompts naturally a conjecture in the instanton context.”