Bordered Heegaard Floer homology /
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| Author / Creator: | Lipshitz, R. (Robert), author. |
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| Imprint: | Providence, RI : American Mathematical Society, [2018] |
| Description: | viii, 279 pages illustrations (some color) ; 26 cm. |
| Language: | English |
| Series: | Memoirs of the American Mathematical Society, 0065-9266 ; number 1216 Memoirs of the American Mathematical Society ; no. 1216. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11682970 |
| Summary: | 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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| Item Description: | "July 2018, volume 254, number 1216 (fourth of 5 numbers)." |
| Physical Description: | viii, 279 pages illustrations (some color) ; 26 cm. |
| Bibliography: | Includes bibliographical references (pages 269-272) and index. |
| ISBN: | 9781470428884 1470428881 |
| ISSN: | 0065-9266 ; |
