منابع مشابه
Heegaard diagrams and Floer homology
We review the construction of Heegaard–Floer homology for closed three-manifolds and also for knots and links in the three-sphere. We also discuss three applications of this invariant to knot theory: studying the Thurston norm of a link complement, the slice genus of a knot, and the unknotting number of a knot. We emphasize the application to the Thurston norm, and illustrate the theory in the ...
متن کاملHow a strongly irreducible Heegaard splitting intersects a handlebody
In [Topology Appl. 90 (1998) 135] Scharleman showed that a strongly irreducible Heegaard splitting surface Q of a 3-manifold M can, under reasonable side conditions, intersect a ball or a solid torus in M in only a few possible ways. Here we extend those results to describe how Q can intersect a handlebody inM . 2001 Elsevier Science B.V. All rights reserved.
متن کاملHeegaard diagrams and holomorphic disks
Gromov’s theory of pseudo-holomorphic disks [39] has wide-reaching consequences in symplectic geometry and low-dimensional topology. Our aim here is to describe certain invariants for low-dimensional manifolds built on this theory. The invariants we describe here associate a graded Abelian group to each closed, oriented three-manifold Y , the Heegaard Floer homology of Y . These invariants also...
متن کاملSutured Heegaard diagrams for knots
We define sutured Heegaard diagrams for null-homologous knots in 3–manifolds. These diagrams are useful for computing the knot Floer homology at the top filtration level. As an application, we give a formula for the knot Floer homology of a Murasugi sum. Our result echoes Gabai’s earlier works. We also show that for socalled “semifibred" satellite knots, the top filtration term of the knot Floe...
متن کاملGrid Diagrams and Heegaard Floer Invariants
We give combinatorial descriptions of the Heegaard Floer homology groups for arbitrary three-manifolds (with coefficients in Z/2Z). The descriptions are based on presenting the three-manifold as an integer surgery on a link in the three-sphere, and then using a grid diagram for the link. We also give combinatorial descriptions of the mod 2 Ozsváth-Szabó mixed invariants of closed four-manifolds...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2003
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(02)00142-6