Holomorphic discs and sutured manifolds

By Andr'as Juh'asz. 2006

254 citations recorded by the source corpus.

In this paper we construct a Floer-homology invariant for a natural and wide class of sutured manifolds that we call balanced. This generalizes the Heegaard Floer hat theory of closed three-manifolds and links. Our invariant is unchanged under product decompositions and is zero for nontaut sutured manifolds. As an application, an invariant of Seifert surfaces is given and is computed in a few interesting cases.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c91ac2aef7a800d43e8c3854462e597fe384797d

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Citations in the corpus

Khovanov homology is an unknot-detector (2010, methodology): “The construction of KHI (K) in [24] was motivated by Juhász’s work on sutured manifolds in the setting of Heegaard Floer theory [13, 14]: in the context of sutured manifolds, KHI (K) can be defined as”
On the Colored Jones Polynomial, Sutured Floer homology, and Knot Floer homology (2008, methodology): “15 of [7], we know that SFH(Yη(Ii),η(Ii+1)) = V ⊗j , where V = Z2 ⊕ Z2.”
Sutures and contact homology I (2010, methodology): “Juhász’ work also motivated the definition of a sutured version of SeibergWitten Floer homology by Kronheimer and Mrowka [KM].”
Instanton Floer homology and the Alexander polynomial (2009, methodology): “We recall the definition of the instanton Floer homology for a balanced sutured manifold, as introduced in [8] with motivation from the Heegaard counterpart defined in [4].”
The vanishing of the contact invariant in the presence of torsion (2007, background): “Recently, Honda, Kazez and Mati´c [HKM3] defined an invariant of a contact 3-manifold with convex boundary as an element of Juh´asz’ sutured Floer homology [ Ju1 , Ju2].”
Knot Floer homology detects fibred knots (2006, methodology): “Later on, Juhász introduced an invariant for sutured manifolds, called “sutured Floer homology”, and proved some properties [11].”
The sutured Floer homology polytope (2008, methodology): “M; /, which was introduced in [13]; also see my paper[14].”
Knot Floer homology detects fibred knots (2007, methodology): “Later on, Juhász introduced an invariant for sutured manifolds, called “sutured Floer homology”, and proved some properties [11].”
Heegard Floer invariants of Legendrian knots in contact three-manifolds (2008, result): “(b) We also note that recent work of Honda–Kazez–Matić [20] provides another invariant for Legendrian knots L ⊂ (Y, ξ) through the sutured contact invariant of an appropriate complement of L in Y , using the sutured Floer homology of Juhász [21].”
The contact invariant in sutured Floer homology (2007, background): “In a pair of important papers [ Ju1 , Ju2], Andr´as Juh´asz generalized (the hat versions of)”
Floer simple manifolds and L-space intervals (2015, unknown): “Let us write V 0 s := ĤFK(Kμ, s), so we have a decomposition V 0 ≃ ⊕sV 0 s , and similarly for V (1), where the indexing sets in the sums are Spin(Y, γμ) and Spin (Y, γλ), as defined in [25].”
Annular Khovanov homology and knotted Schur–Weyl representations (2015, background): “[13], [12]) with Juhász’s sutured version of Heegaard Floer homology [20].”
Floer homology and surface decompositions (2006, methodology): “In [7] we defined a Floer homology invariant for balanced sutured manifolds.”
Contact structures, sutured Floer homology and TQFT (2008, methodology): “In Section 2 we review the notions of sutured Floer homology and partial open book decompositions, which appeared in [ Ju1 , Ju2, HKM3].”
Knots, sutures, and excision (2008, background): “G T ] 3 1 Contents 1 Introduction 1 2 Background on monopole Floer homology 3 3 Floer’s excision theorem 19 4 Monopole Floer homology for sutured manifolds 26 5 Knot homology 33 6 Fibered knots 41 7 Instantons 52”