478 citations · 2.5k across the 62 of their papers we have counts for
45 papers · 1 filter
Planar graphs deformations of bordered knot algebras
Peter Ozsvath, Zoltan Szabo
In an earlier paper, we introduced ``bordered knot algebras'', which are graded algebras indexed by a pair of integers (m,k). In a subsequent paper, we introduced a two-parameter f…
Exotic definite four-manifolds with non-trivial fundamental group
Andras I. Stipsicz, Zoltan Szabo
Inspired by a recent result of Levine-Lidman-Piccirillo, we construct infinitely many exotic smooth structures on some closed four-manifolds with definite intersection form and fun…
The pong algebra
Peter S. Ozsvath, Zoltan Szabo
In an earlier paper, we described bordered algebras for knot Floer homology. In this paper, we introduce a differential graded algebra, the pong algebra and compute the A-infinity…
A note on thickness of knots
Andras I. Stipsicz, Zoltan Szabo
We introduce a numerical invariant β(K) of a knot K which measures how non-alternating K is. We prove an inequality between β(K) and the (knot Floer) thickness of K. As an applicat…
Algebras with matchings and link Floer homology
Peter Ozsvath, Zoltan Szabo
We explain how to use bordered algebras to compute a version of link Floer homology. As a corollary, we also give a fast computation of the Thuston polytope for links in the three-…
Algebras with matchings and knot Floer homology
Zoltan Szabo, Peter Ozsvath
Knot Floer homology is a knot invariant defined using holomorphic curves. In more recent work, taking cues from bordered Floer homology,the authors described another knot invariant…
Bordered knot algebras with matchings
Peter S. Ozsvath, Zoltan Szabo
This paper generalizes the bordered-algebraic knot invariant introduced in an earlier paper, giving an invariant now with more algebraic structure. It also introduces signs to defi…
An overview of knot Floer homology
Peter Ozsvath, Zoltan Szabo
Knot Floer homology is an invariant for knots discovered by the authors and, independently, Jacob Rasmussen. The discovery of this invariant grew naturally out of studying how a ce…
Kauffman states, bordered algebras, and a bigraded knot invariant
Peter Ozsvath, Zoltan Szabo
We define and study a bigraded knot invariant whose Euler characteristic is the Alexander polynomial, closely connected to knot Floer homology. The invariant is the homology of a c…
Unoriented knot Floer homology and the unoriented four-ball genus
Peter Ozsvath, Andras Stipsicz, Zoltan Szabo
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 th…
A perturbation of the geometric spectral sequence in Khovanov homology
Sucharit Sarkar, Cotton Seed, Zoltan Szabo
We study the relationship between Bar-Natan's perturbation in Khovanov homology and Szabo's geometric spectral sequence, and construct a link invariant that generalizes both into a…
Concordance homomorphisms from knot Floer homology
Peter Ozsvath, Andras Stipsicz, Zoltan Szabo
We modify the construction of knot Floer homology to produce a one-parameter family of homologies for knots in the three-sphere. These invariants can be used to give homomorphisms…
A geometric spectral sequence in Khovanov homology
Zoltan Szabo
The aim of this paper is to introduce and study a geometric spectral sequence in Khovanov homology. The construction was motivated by a similar spectral sequence from Khovanov homo…
Combinatorial Heegaard Floer homology and nice Heegaard diagrams
Peter S. Ozsvath, Andras I. Stipsicz, Zoltan Szabo
We consider a stabilized version of hat Heegaard Floer homology of a 3-manifold Y (i.e. the U=0 variant of Heegaard Floer homology for closed 3-manifolds). We give a combinatorial…
A combinatorial description of the version of Heegaard Floer homology
Peter Ozsvath, Andras Stipsicz, Zoltan Szabo
We show that every 3--manifold admits a Heegaard diagram in which a truncated version of Heegaard Floer homology (when the holomorpic disks pass through the basepoints at most once…
On the skein exact squence for knot Floer homology
Peter Ozsvath, Zoltan Szabo
The aim of this paper is to study the skein exact sequence for knot Floer homology. We prove precise graded version of this sequence, and also one using $\HFm$. Moreover, a complet…
A cube of resolutions for knot Floer homology
Peter Ozsvath, Zoltan Szabo
We develop a skein exact sequence for knot Floer homology, involving singular knots. This leads to an explicit, algebraic description of knot Floer homology in terms of a braid pro…
Floer homology and singular knots
Peter Ozsvath, Andras I. Stipsicz, Zoltan Szabo
We define Floer homology theories for oriented, singular knots in S^3 and show that one of these theories can be defined combinatorially for planar singular knots.
Legendrian knots, transverse knots and combinatorial Floer homology
Peter Ozsvath, Zoltan Szabo, Dylan Thurston
Using the combinatorial approach to knot Floer homology, we define an invariant for Legendrian knots in the three-sphere, which takes values in link Floer homology. This invariant…
Rational blow-downs and smoothings of surface singularities
Andras I. Stipsicz, Zoltan Szabo, Jonathan Wahl
In this paper we give a necessary combinatorial condition for a negative--definite plumbing tree to be suitable for rational blow--down, or to be the graph of a complex surface sin…
On combinatorial link Floer homology
Ciprian Manolescu, Peter Ozsvath, Zoltan Szabo +1
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 descripti…
The Dehn surgery characterization of the trefoil and the figure eight knot
Peter Ozsvath, Zoltan Szabo
We give a Dehn surgery characterization of the trefoil and the figure eight knots. These results are gotten by combining surgery formulas in Heegaard Floer homology from an earlier…
Heegaard diagrams and Floer homology
Peter Ozsvath, Zoltan Szabo
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 invari…
Link Floer homology and the Thurston norm
Peter Ozsvath, Zoltan Szabo
We show that link Floer homology detects the Thurston norm of a link complement. As an application, we show that the Thurston polytope of an alternating link is dual to the Newton…