TY  - BOOK
AU  - Ozsvath,Peter S.
AU  - Stipsicz,Andras I.
AU  - Szabo,Zoltan
TI  - Grid homology for knots and links
T2  - Mathematical surveys and monographs
SN  - 9781470417376 (alk. paper)
U1  - 510MS 23
PY  - 2015///
CY  - Providence :        
PB  - American Mathematical Society,  
KW  - Knot theory
KW  - Link theory
KW  - Homology theory
N1  - 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
N2  - 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.
ER  -