Related papers: The Seiberg-Witten equations for multiple-spinors …
We prove a diagonalisation theorem for the tautological, or generalised Miller-Morita-Mumford classes of compact, smooth, simply-connected definite $4$-manifolds. Our result can be thought of as a families version of Donaldson's…
We demonstrate an obstruction to finding certain splittings of four-manifolds along sufficiently twisted circle bundles over Riemann surfaces, arising from Seiberg-Witten theory. These obstructions are used to show a non-splitting result…
Noncommutative versions of theories with a gauge freedom define (when they exist) consistent deformations of their commutative counterparts. General aspects of Seiberg-Witten maps are discussed from this point of view. In particular, the…
Fundamental group of a manifold gives a deep effect on its underlying smooth structure. In this paper we introduce a new variant of the Donaldson invariant in Yang-Mills gauge theory from twisting by the Picard group of a four manifold in…
We present a non-abelian generalization of Witten monopole equations and we analyze the associated moduli problem, which can be regarded as a generalization of Donaldson theory. The moduli space of solutions for SU(2) monopoles on K\"ahler…
We prove structure theorems for the Donaldson invariants of 4-manifolds with b_+=1, similar to those of Kronheimer and Mrowka in the case b_+>1: We show that for a 4-manifold with b_+=1 and two different period points F, G on the boundary…
We solve a conjecture of Morgan and Szabo (Embedded genus 2 surfaces in four-manifolds, Preprint) about the relationship of the basic classes of two four-manifolds $X_i$ of simple type with $b_1=0$, $b^+>1$, such that there are embedded…
Seiberg-Witten solutions of four-dimensional supersymmetric gauge theories possess rich but involved integrable structures. The goal of this paper is to show that an isomonodromy problem provides a unified framework for understanding those…
By studying the Seiberg-Witten equations on end-periodic manifolds, we give an obstruction on the existence of positive scalar curvature metric on compact $4$-manifolds with the same homology as $S^{1}\times S^{3}$. This obstruction is…
We present a summary of the progress made in the last few years on topological quantum field theory in four dimensions. In particular, we describe the role played by duality in the developments which led to the Seiberg-Witten invariants and…
We proceed to derive equations for the symmetric tensor of the second rank on the basis of the Bargmann-Wigner formalism in a straightforward way. The symmetric multispinor of the fourth rank is used. It is constructed out of the Dirac…
We present the simplest non-abelian version of Seiberg-Witten theory: Quaternionic monopoles. These monopoles are associated with Spin^h(4)-structures on 4-manifolds and form finite-dimensional moduli spaces. On a Kahler surface the…
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.…
In this paper connections between different gauge-theoretical problems in high and low dimensions are established. In particular it is shown that higher dimensional asd equations on total spaces of spinor bundles over low dimensional…
We give an infinite family of embeddings of $\mathbb{R} P^2$ to $S^4$ such that they are mutually topologically isotopic however are not smoothly isotopic to each other. Moreover, they are topologically isotopic to the standard $P^2$-knot.…
The adiabatic limit procedure associates with every solution of Abelian Higgs model in (2+1) dimensions a geodesic in the moduli space of static solutions. We show that the same procedure for Seiberg--Witten equations on 4-dimensional…
In the second of a pair of papers, we complete the construction of Seiberg-Witten-like invariants for smooth four-manifolds equipped with broken fibrations, prove an index formula, and compute some examples.
In these notes, we carefully analyze the properties of the "ramified" Seiberg-Witten equations associated with supersymmetric configurations of the Seiberg-Witten abelian gauge theory with surface operators on an oriented closed…
We present an explicit expression for the topological invariants associated to $SU(2)$ monopoles in the fundamental representation on spin four-manifolds. The computation of these invariants is based on the analysis of their corresponding…
In a pair of papers, we construct invariants for smooth four-manifolds equipped with `broken fibrations' - the singular Lefschetz fibrations of Auroux, Donaldson and Katzarkov - generalising the Donaldson-Smith invariants for Lefschetz…