Free Delivery Over $100
|
|
|||
|
||||
OverviewThe 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. Full Product DetailsAuthor: Robert Lipshitz , Peter S. Ozsvath , Mariusz UrbanskiPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.523kg ISBN: 9781470428884ISBN 10: 1470428881 Pages: 276 Publication Date: 30 July 2018 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction; $\mathcal A_\infty$ structures; The algebra associated to a pointed matched circle; Bordered Heegaard diagrams; Moduli spaces; Type $D$ modules; Type $A$ modules; Pairing theorem via nice diagrams; Pairing theorem via time dilation; Gradings; Bordered manifolds with torus boundary; Appendix A. Bimodules and change of framing; Index of definitions; Bibliography.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
||||
