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4-manifolds and Kirby calculus
4-manifolds: Introduction Surfaces in 4-manifolds Complex surfaces Kirby calculus: Handelbodies and Kirby diagrams Kirby calculus More examples Applications: Branched covers and resolutions Elliptic
Heegard Floer invariants of Legendrian knots in contact three-manifolds
We define invariants of null–homologous Legendrian and transverse knots in contact 3–manifolds. The invariants are determined by elements of the knot Floer homology of the underlying smooth knot.
Grid Homology for Knots and Links
* Introduction* Knots and links in $S^3$* Grid diagrams* Grid homology* The invariance of grid homology* The unknotting number and $\tau$* Basic properties of grid homology* The slice genus and
Concordance homomorphisms from knot Floer homology
Abstract We modify the construction of knot Floer homology to produce a one-parameter family of homologies tHFK for knots in S 3 . These invariants can be used to give homomorphisms from the smooth
Ozsvath-Szabo invariants and tight contact three-manifolds, I
Let S 3 r (K) be the oriented 3-manifold obtained by rational r-surgery on a knot K ⊂ S 3 . Using the contact Ozsvath-SzabO invariants we prove, for a class of knots K containing all the algebraic
Indecomposability of certain Lefschetz fibrations
We prove that Lefschetz fibrations admitting a section of square -1 cannot be decomposed as fiber sums. In particular, Lefschetz fibrations on symplectic 4-manifolds found by Donaldson are
Surgery diagrams for contact 3-manifolds
In two previous papers, the two first-named authors introduced a notion of contact r-surgery along Legendrian knots in contact 3-manifolds. They also showed how (at least in principle) to convert any
Surgery on Contact 3-Manifolds and Stein Surfaces
1. Introduction.- 2. Topological Surgeries.- 3. Symplectic 4-Manifolds.- 4. Contact 3-Manifolds.- 5. Convex Surfaces in Contact 3-Manifolds.- 6. Spinc Structures on 3- and 4-Manifolds.- 7. Symplectic
Contact surgeries and the transverse invariant in knot Floer homology
Abstract We study naturality properties of the transverse invariant in knot Floer homology under contact (+1)-surgery. This can be used as a calculational tool for the transverse invariant. As a
Unoriented knot Floer homology and the unoriented four-ball genus
In an earlier work, we introduced a family of t-modified knot Floer homologies, defined by modifying the construction of knot Floer homology HFK-minus. The resulting groups were then used to define