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We define a Floer-homology invariant for links in S, and study its properties.

- Zoltán Szabó
- 2001

In this paper, we demonstrate a relation among Seiberg-Witten invariants which arises from embedded surfaces in four-manifolds whose self-intersection number is negative. These relations, together with Taubes’ basic theorems on the Seiberg-Witten invariants of symplectic manifolds, are then used to prove the symplectic Thom conjecture: a symplectic surface… (More)

Suppose that X is a smooth closed oriented 4-manifold, and that X contains a smoothly embedded 2-torus T 2 ↪→ X with trivial self-intersection number. Similarly to Dehn-surgery on knots in 3-manifolds, a generalized logarithmic transformation of X along T 2 is defined by deleting a tubular neighborhood of T 2 from X and gluing it back via a diffeomorphism φ… (More)

- Ciprian Manolescu, Peter Steven Ozsváth, +5 authors Dylan Thurston
- 2007

Link Floer homology is an invariant for links defined using a suitable version of Lagrangian Floer homology. In an earlier paper, this invariant was given a combinatorial description with mod 2 coefficients. In the present paper, we give a self-contained presentation of the basic properties of link Floer homology, including an elementary proof of its… (More)

We calculate the Heegaard Floer homologies for three-manifolds obtained by plumbings of spheres specified by certain graphs. Our class of graphs is sufficiently large to describe, for example, all Seifert fibered rational homology spheres. These calculations can be used to determine also these groups for other three-manifolds, including the product of a… (More)

- Zoltán Szabó
- Random Struct. Algorithms
- 1990

The van der Waerden number W(n) is the smallest integer so that if we divide the integers {1,2, . . . , W(n)} into two classes, then at least one of them contains an arithmetic progression of length n. We prove in this paper that W(n) 2 2"/n" for all sufficiently large n.

- Jongil Park, András I. Stipsicz, Zoltán Szabó
- 2004

Motivated by a construction of Fintushel and Stern, we show that the topological 4–manifold CP#5CP2 supports infinitely many distinct smooth structures. AMS Classification 53D05, 14J26; 57R55, 57R57

- András I Stipsicz, Zoltán Szabó
- 2005

We construct smooth 4–manifolds homeomorphic but not diffeomorphic to CP#6CP2 . AMS Classification numbers Primary: 53D05, 14J26 Secondary: 57R55, 57R57

- Paolo Lisca, Peter Steven Ozsváth, András I. Stipsicz, Zoltán Szabó
- 2009

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. We compute these invariants, showing that they do not vanish, for certain non– loose knots in overtwisted 3–spheres. Moreover, we apply the invariants to find… (More)

- Julia L. Barringer, Zoltán Szabó, D. Schneider, William D. Atkinson, Robert A Gallagher
- The Science of the total environment
- 2006

Water samples were collected from domestic wells at an unsewered residential area in Gloucester County, New Jersey where mercury (Hg) concentrations in well water were known to exceed the USEPA maximum contaminant level (MCL) of 2,000 ng/L. This residential area (the CSL site) is representative of more than 70 such areas in southern New Jersey where about… (More)