Related papers: Yang-Mills Connections On Orientable and Nonorient…

We present a new construction of tubular neighborhoods in (possibly infinite dimensional) Riemannian manifolds M, which allows us to show that if G is an arbitrary group acting isometrically on M, then every G-invariant submanifold with…

Let $\Sigma$ be a closed surface, $G$ a compact Lie group, with Lie algebra $g$, $\xi \colon P \to \Sigma$ a principal $G$-bundle, let $N(\xi)$ denote the moduli space of central Yang-Mills connections on $\xi$, for suitably chosen…

The first and shorter part of this thesis deals with the structural assumption of invertibility in a Lie groupoid. When this assumption is dropped, we obtain the notion of a Lie category: a small category, endowed with a compatible…

Refinements of the Yang-Mills stratifications of spaces of connections over a compact Riemann surface are investigated. The motivation for this study was the search for a complete set of relations between the standard generators for the…

In this paper we study (static) solutions of the rank 2 Yang-Mills-Higgs equations on the Riemann sphere, with concical singularities, that bifurcate from constant curvature connections. We focus attention on the case where there are…

We study the gradient flow lines of a Yang-Mills-type functional on the space of gauged holomorphic maps $\mathcal{H}(P,X)$, where $P$ is a principal bundle on a Riemann surface $\Sigma$ and $X$ is a K\"ahler Hamiltonian $G$-manifold. For…

This paper aims to develop a non-commutative geometrical version of the theory of Yang--Mills--Scalar--Matter fields. To accomplish this purpose, we will dualize the geometrical formulation of this theory, in which principal $G$--bundles,…

We construct one Yang-Mills measure on a compact surface for each isomorphism class of principal bundles over this surface. For this, we define a new discrete gauge theory which is essentially a covering of the usual one. We prove that the…

Let G be a Lie goup, let M and N be smooth connected G-manifolds, let f be a smooth G-map from M to N, and let P denote the fiber of f. Given a closed and equivariantly closed relative 2-form for f with integral periods, we construct the…

Studied are the moduli spaces of Yang-Mills connections on finitely generated projective modules associated with noncommutative flows. It is actually shown that they are homeomorphic to those on the dual modules associated with the dual…

Fix a $C^\infty$ principal $G$--bundle $E^0_G$ on a compact connected Riemann surface $X$, where $G$ is a connected complex reductive linear algebraic group. We consider the gradient flow of the Yang--Mills--Higgs functional on the…

We study the Morse theory of the Yang-Mills-Higgs functional on the space of pairs $(A,\Phi)$, where $A$ is a unitary connection on a rank 2 hermitian vector bundle over a compact Riemann surface, and $\Phi$ is a holomorphic section of $(E,…

We study the Yang-Mills flow on a holomorphic vector bundle E over a compact Kahler manifold X . Along a solution of the flow, we show the curvature $i\Lambda F(A_t)$ approaches in $L^2$ an endomorphism with constant eigenvalues given by…

We study the moduli space of Yang--Mills connections on bundles over a conformally compact manifold $\overline{M}$. We prove that, for every Yang--Mills connection $A$ that satisfies an appropriate nondegeneracy condition, and for every…

If we consider the moduli space of flat connections of a non trivial principal SO(3)-bundle over a surface, then we can define a map from the set of perturbed closed geodesics, below a given energy level, into families of perturbed…

We study a topological Yang-Mills theory with $N=2$ fermionic symmetry. Our formalism is a field theoretical interpretation of the Donaldson polynomial invariants on compact K\"{a}hler surfaces. We also study an analogous theory on compact…

We construct off-shell vertex operators for the bosonic spinning particle. Using the language of homotopy algebras, we show that the full nonlinear structure of Yang-Mills theory, including its gauge transformations, is encoded in the…

The non-local generalized two dimensional Yang Mills theories on an arbitrary orientable and non-orientable surfaces with boundaries is studied. We obtain the effective action of these theories for the case which the gauge group is near the…

In this paper we show the existence of non minimal critical points of the Yang-Mills functional over a certain family of 4-manifolds with generic SU(2)-invariant metrics using Morse and homotopy theoretic methods. These manifolds are acted…

For analyzing stationary Yang-Mills connections in higher dimensions, one has to work with Morrey-Sobolev bundles and connections. The transition maps for a Morrey-Sobolev principal $G$-bundles are not continuous and thus the usual notion…