
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 |

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 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 254; 2018; 279 ppMSC: 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.
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Table of Contents
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Chapters
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1. Introduction
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2. $\mathcal {A}_{\infty }$ structures
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3. The algebra associated to a pointed matched circle
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4. Bordered Heegaard diagrams
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5. Moduli spaces
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6. Type $D$ modules
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7. Type $A$ modules
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8. Pairing theorem via nice diagrams
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9. Pairing theorem via time dilation
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10. Gradings
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11. Bordered manifolds with torus boundary
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A. Bimodules and change of framing
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Additional Material
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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
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A. Bimodules and change of framing