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Bordered Heegaard Floer Homology
 
Robert Lipshitz University of Oregon, Eugene, Oregon, USA
Peter Ozsváth Princeton University, Princeton, New Jersey, USA
Dylan P. Thurston Indiana University, Bloomington, Indiana, USA
Bordered Heegaard Floer Homology
eBook ISBN:  978-1-4704-4748-9
Product Code:  MEMO/254/1216.E
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
Bordered Heegaard Floer Homology
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Bordered Heegaard Floer Homology
Robert Lipshitz University of Oregon, Eugene, Oregon, USA
Peter Ozsváth Princeton University, Princeton, New Jersey, USA
Dylan P. Thurston Indiana University, Bloomington, Indiana, USA
eBook ISBN:  978-1-4704-4748-9
Product Code:  MEMO/254/1216.E
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2542018; 279 pp
    MSC: Primary 57

    The authors construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with parametrized boundary, the invariant comes in two different versions, one of which (type \(D\)) is a module over the algebra and the other of which (type \(A\)) is an \(\mathcal A_\infty\) module. Both are well-defined up to chain homotopy equivalence. For a decomposition of a 3-manifold into two pieces, the \(\mathcal A_\infty\) tensor product of the type \(D\) module of one piece and the type \(A\) module from the other piece is \(\widehat{HF}\) of the glued manifold.

    As a special case of the construction, the authors specialize to the case of three-manifolds with torus boundary. This case can be used to give another proof of the surgery exact triangle for \(\widehat{HF}\). The authors relate the bordered Floer homology of a three-manifold with torus boundary with the knot Floer homology of a filling.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. $\mathcal {A}_{\infty }$ structures
    • 3. The algebra associated to a pointed matched circle
    • 4. Bordered Heegaard diagrams
    • 5. Moduli spaces
    • 6. Type $D$ modules
    • 7. Type $A$ modules
    • 8. Pairing theorem via nice diagrams
    • 9. Pairing theorem via time dilation
    • 10. Gradings
    • 11. Bordered manifolds with torus boundary
    • A. Bimodules and change of framing
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2542018; 279 pp
MSC: Primary 57

The authors construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with parametrized boundary, the invariant comes in two different versions, one of which (type \(D\)) is a module over the algebra and the other of which (type \(A\)) is an \(\mathcal A_\infty\) module. Both are well-defined up to chain homotopy equivalence. For a decomposition of a 3-manifold into two pieces, the \(\mathcal A_\infty\) tensor product of the type \(D\) module of one piece and the type \(A\) module from the other piece is \(\widehat{HF}\) of the glued manifold.

As a special case of the construction, the authors specialize to the case of three-manifolds with torus boundary. This case can be used to give another proof of the surgery exact triangle for \(\widehat{HF}\). The authors relate the bordered Floer homology of a three-manifold with torus boundary with the knot Floer homology of a filling.

  • Chapters
  • 1. Introduction
  • 2. $\mathcal {A}_{\infty }$ structures
  • 3. The algebra associated to a pointed matched circle
  • 4. Bordered Heegaard diagrams
  • 5. Moduli spaces
  • 6. Type $D$ modules
  • 7. Type $A$ modules
  • 8. Pairing theorem via nice diagrams
  • 9. Pairing theorem via time dilation
  • 10. Gradings
  • 11. Bordered manifolds with torus boundary
  • A. Bimodules and change of framing
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.