Grid homology for knots and links / Peter S. Ozsvath, Andras I. Stipsicz and Zoltan Szabo.
Material type:
TextSeries: Mathematical surveys and monographs ; v 208.Publication details: Providence : American Mathematical Society, 2015.Description: x, 410 p. : illustrations ; 27 cmISBN: - 9781470417376 (alk. paper)
- 510MS 23 Am512
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 510MS Am512 (Browse shelf(Opens below)) | Available | 136733 |
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| 510MS Am512 Nonlinear elliptic equations and nonassociative algebras / | 510MS Am512 Topological modular forms / | 510MS Am512 Tensor categories / | 510MS Am512 Grid homology for knots and links / | 510MS Am512 Ricci flow : | 510MS Am512 Persistence theory : from quiver representations to data analysis / | 510MS Am512 Fokker-Planck-Kolmogorov equations / |
Includes bibliographical references and index.
1. Introduction --
2. Knots and links in S3 --
3. Grid diagrams --
4. Grid homology --
5. The invariance of grid homology --
6. The unknotting number and tau --
7. Basic properties of grid homology --
8. The slice genus and tau --
9. The oriented skein exact sequence --
10. Grid homologies of alternating knots --
11. Grid homology for links --
12. Invariants of Legendrian and transverse knots --
13. The filtered grid complex --
14. More on the filtered chain complex --
15. Grid homology over the integers --
16. The holomorphic theory --
17. Open problems --
Appendixes --
Bibliography --
Index.
The book gives a self-contained treatment of knot Floer homology from the point of view of grid diagrams. Applications include computations of the unknotting number and slice genus of torus knots (asked first in the 1960s and settled in the 1990s), and tools to study variants of knot theory in the presence of a contact structure. Additional topics are presented to prepare readers for further study in holomorphic methods in low-dimensional topology, especially Heegaard Floer homology.
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