Related papers: Witten's conjecture for many four-manifolds of sim…

Let $X$ be a smooth, closed, connected, orientable four-manifold with $b^1(X)=0$ and $b^+(X)\geq 3$ and odd. We show that if $X$ has Seiberg-Witten simple type, then the SO(3)-monopole cobordism formula of Feehan and Leness (2002) implies…

Witten's conjecture suggests that the polynomial invariants of Donaldson are expressible in terms of the Seiberg-Witten invariants if the underlying four-manifold is of simple type. A higher rank version of the Donaldson invariants was…

We show that the SO(3) monopole cobordism formula from Feehan and Leness (2002) implies that all smooth, closed, oriented four-manifolds with $b^1=0$ and $b^+\geq 3$ and odd with Seiberg-Witten simple type satisfy the superconformal simple…

We propose an explicit formula connecting Donaldson invariants and Seiberg-Witten invariants of a 4-manifold of simple type via Nekrasov's deformed partition function for the N=2 SUSY gauge theory with a single fundamental matter. This…

We prove Witten's formula relating the Donaldson and Seiberg-Witten series modulo powers of degree $c+2$, with $c=-{1/4}(7\chi+11\sigma)$, for four-manifolds obeying some mild conditions, where $\chi$ and $\sigma$ are their Euler…

In this article we complete the proof---for a broad class of four-manifolds---of Witten's conjecture that the Donaldson and Seiberg-Witten series coincide, at least through terms of degree less than or equal to c-2, where c is a linear…

We generalize Witten's conjectured formula relating Donaldson and Seiberg-Witten invariants to manifolds of non-simple type, via equivariant localization techniques. This approach does not use the theory of non-abelian monopoles, but works…

We prove an analogue of the Kotschick-Morgan conjecture in the context of SO(3) monopoles, obtaining a formula relating the Donaldson and Seiberg-Witten invariants of smooth four-manifolds using the SO(3)-monopole cobordism. The main…

A famous conjecture in gauge theory mathematics, attributed to Witten, suggests that the polynomial invariants of Donaldson are expressible in terms of the Seiberg-Witten invariants if the underlying four-manifold is of simple type.…

We prove that, under a simple condition on the cohomology ring, every closed 4-manifold has mod 2 Seiberg-Witten simple type. This result shows that there exists a large class of topological 4-manifolds such that all smooth structures have…

A proof via the Seiberg-Witten moduli space of Donaldson's theorem on smooth 4-manifolds with definite intersection forms.

This article is based on a lecture by the first author at the International Georgia Topology Conference 2001 (Athens, Georgia) and the Mathematische Arbeitstagung 2001 (Bonn, Germany). We sketch a proof of Witten's formula relating the…

Recently, motivated by supersymmetric gauge theory, Cachazo, Douglas, Seiberg, and Witten proposed a conjecture about finite dimensional simple Lie algebras, and checked it in the classical cases. Later V. Kac and the author proposed a…

In this article we show that some of the recent results of Marino, Moore, and Peradze (math.DG/9812042, hep-th/9812055) -- in particular their conjecture that all closed, smooth four-manifolds with b_2^+ > 1 (and Seiberg-Witten simple type)…

In this note, we present a proof of Donaldson's Diagonalization Theorem via an abelian gauge-theoretic variant of the Seiberg-Witten equations for multiple spinors. Like the other proof of Donaldson's theorem using the standard…

This is the third installment in our series of articles (dg-ga/9712005, dg-ga/9710032) on the application of the PU(2) monopole equations to prove Witten's conjecture (hep-th/9411102) concerning the relation between the Donaldson and…

We prove that every suitable $4$-manifold with $b_1=0$ and with an embedded Riemann surface of genus $2$ is of simple type. We find a relationship between the basic classes of two of these $4$-manifolds and those of the connected sum along…

Using quantum field-theoretic arguments, Witten has established a relation between the Donaldson and Seiberg-Witten invariants of smooth four-manifolds. In this survey article, we describe the program to prove this relation using a moduli…

The present article is the first in a series whose ultimate goal is to prove the Kotschick-Morgan conjecture concerning the wall-crossing formula for the Donaldson invariants of a four-manifold with b^+ = 1. The conjecture asserts that the…

Casson-type invariants emerging from Donaldson theory over certain negative definite 4-manifolds were recently suggested by Andrei Teleman. These are defined by a count of a zero-dimensional moduli space of flat instantons. Motivated by the…