Holomorphic disks and three-manifold invariants: properties and applications

Abstract

In an earlier paper (math.SG/0101206), we introduced Floer homology theories associated to closed, oriented three-manifolds Y and SpinC structures. In the present paper, we give calculations and study the properties of these invariants. The calculations suggest a conjectured relationship with Seiberg-Witten theory. The properties include a relationship between the Euler characteristics of these theories and Turaev's torsion, a relationship with the minimal genus problem (Thurston norm), and surgery exact sequences. We also include some applications of these techniques to three-manifold topology.

87 pages, 12 figures. To appear in Annals of Mathematics. Reorganized both this paper and its prequel, math.SG/0101206

References in corpus (5)

• Seiberg-Witten-Floer stable homotopy type of three-manifolds with b_1=0
• Holomorphic triangles and invariants for smooth four-manifolds
• Periodic Floer pro-spectra from the Seiberg-Witten equations
• Holomorphic disks and topological invariants for closed three-manifolds
• The Theta Divisor and Three-Manifold Invariants

Cited by in corpus (62)

• On the Floer homology of plumbed three-manifolds
• Heegaard Floer homology and alternating knots
• Bordered Heegaard Floer homology: Invariance and pairing
• Concordance homomorphisms from knot Floer homology
• Fivebranes and 3-manifold homology
• HF=HM I : Heegaard Floer homology and Seiberg--Witten Floer homology
• Heegaard Floer homologies and contact structures
• Ozsvath-Szabo invariants and tight contact three-manifolds, I
• Khovanov module and the detection of unlinks
• The periodic Floer homology of a Dehn twist
• A note on cabling and L-space surgeries
• A spanning tree model for the Heegaard Floer homology of a branched double-cover
• On the existence of tight contact structures on Seifert fibered 3-manifolds
• Product Formulae for Ozsvath-Szabo 4-manifold Invariants
• Holomorphic triangles and invariants for smooth four-manifolds
• Splicing knot complements and bordered Floer homology
• Seifert fibered contact three-manifolds via surgery
• Khovanov homology, sutured Floer homology, and annular links
• Combinatorial cobordism maps in hat Heegaard Floer theory
• Monopoles and lens space surgeries
• A splitting theorem for the Seiberg-Witten invariant of a homology $S^1\times S^3$
• $L$-space surgeries on links
• A tour of bordered Floer theory
• Cuspidal curves and Heegaard Floer homology
• Sutured Floer homology and invariants of Legendrian and transverse knots
• Joining and gluing sutured Floer homology
• $\tau$-invariants for knots in rational homology spheres
• Dehn Twists in Heegaard Floer Homology
• Holomorphic disks and topological invariants for closed three-manifolds
• Floer homology and splicing knot complements
• The decategorification of bordered Heegaard Floer homology
• Knot Floer homology, genus bounds, and mutation
• On the equivalence of contact invariants in sutured Floer homology theories
• Heegaard Floer homology of surgeries on two-bridge links
• Holomorphic disks and knot invariants
• Strong Heegaard diagrams and strong L-spaces
• On the Upsilon invariant of cable knots
• An enhanced Euler characteristic of sutured instanton homology
• On the classification of Floer-type theories
• What do Topologists want from Seiberg--Witten theory? (A review of four-dimensional topology for physicists)
• Contact Structures on Plumbed 3-Manifolds
• Instanton Floer homology, sutures, and Euler characteristics
• Ozsvath-Szabo bordered algebras and subquotients of category O
• Knot Floer homology of (1,1)-knots
• Irreducible 3-manifolds that cannot be obtained by 0-surgery on a knot
• An involution acting nontrivially on Heegard-Floer homology
• On the Heegaard Floer homology of branched double-covers
• Khovanov homology detects split links
• Dimensionally-reduced sutured Floer homology as a string homology
• The anti-diagonal filtration: reduced theory and applications
• On mapping cones of Seifert fibered surgeries
• Tight Planar Contact Manifolds with Vanishing Heegaard Floer Contact Invariants
• Knot Complement Problem for L-space $\mathbb{Z}H{S}^3$
• A slicing obstruction from the 10/8 theorem
• Heegaard-Floer homology and string links
• Dehn surgery and non-separating two-spheres
• A self-pairing theorem for tangle Floer homology
• 4-dimensional aspects of tight contact 3-manifolds
• Variants of equivariant Seiberg-Witten Floer homology
• Holomorphic triangle invariants and the topology of symplectic four-manifolds
• Absolutely Graded Floer homologies and intersection forms for four-manifolds with boundary
• Seiberg-Witten-Floer Homology and Gluing Formulae