Bordered Heegaard Floer Homology

Robert Lipshitz, Peter S. Ozsvath, Mariusz Urbanski (Autoren)

Buch | Softcover

276 Seiten

2018
American Mathematical Society (Verlag)
978-1-4704-2888-4 (ISBN)

Infos

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.

Inhalt

Introduction; $/mathcal A_/infty$ 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.

Produkt-Details

• Erscheinungsdatum: 21.09.2018
• Reihe/Serie: Memoirs of the American Mathematical Society
• Verlagsort: Providence
• Sprache: englisch
• Maße: 178 x 254 mm
• Gewicht: 523 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-10: 1-4704-2888-1 / 1470428881
• ISBN-13: 978-1-4704-2888-4 / 9781470428884
• Zustand: Neuware