478 citations · 2.5k across the 62 of their papers we have counts for
7 papers · 1 filter
Isospectral pairs of metrics on balls, spheres, and other manifolds with different local geometries
Z. I. Szabo
The first isospectral pairs of metrics are constructed on balls and spheres. This long standing problem, concerning the existence of such pairs, has been solved by a new method cal…
A cornucopia of isospectral pairs of metrics on spheres with different local geometries
Z. I. Szabo
This article concludes the comprehensive study started in [Sz5], where the first non-trivial isospectral pairs of metrics are constructed on balls and spheres. These investigations…
The theta divisor and the Casson-Walker invariant
Peter Ozsvath, Zoltan Szabo
We use Heegaard decompositions and the theta divisor on a Riemannian surface to define a three-manifold invariant for rational homology three-spheres. This invariant is defined on…
The Theta Divisor and Three-Manifold Invariants
Peter Ozsvath, Zoltan Szabo
In this paper we study an invariant for oriented three-manifolds with , which is defined using Heegaard splittings and the theta divisor of a Riemann surface. The paper is d…
On Embedding Circle-Bundles in Four-Manifolds
Peter Ozsvath, Zoltan Szabo
We demonstrate an obstruction to finding certain splittings of four-manifolds along sufficiently twisted circle bundles over Riemann surfaces, arising from Seiberg-Witten theory. T…
Higher Type Adjunction Inequalities in Seiberg-Witten Theory
Peter Ozsvath, Zoltan Szabo
In this paper, we derive new adjunction inequalities for embedded surfaces with non-negative self-intersection number in four-manifolds. These formulas are proved by using relation…