Let X be a compact connected Riemann surface and EP a holomorphic principal P–bundle over X , where P is a parabolic subgroup of a complex reductive affine algebraic group G. If the Levi bundle associated to EP admits a holomorphic connection, and the reduction EP ⊂ EP × P G is rigid, we prove that EP admits a holomorphic connection. As an immediate consequence, we obtain a sufficient condition...

A stratified bundle is a fibered space in which strata are classical bundles and in which attachment of strata is controlled by a structure category F of fibers. Well known results on fibre bundles are shown to be true for stratified bundles; namely the pull back theorem, the bundle theorem and the principal bundle theorem. AMS SC : 55R55 (Fiberings with singularities); 55R65 (Generalizations o...

The concept of generalised (in the sense of Colombeau) connection on a principal fibre bundle is introduced. This definition is then used to extend results concerning the geometry of principal fibre bundles to those that only have a generalised connection. Some applications to singular solutions of Yang-Mills theory are given. Mathematics Subject Classification (2000): Primary: 46T30; secondary...

Abstract We show that a fibre-preserving self-diffeomorphism which has hyperbolic splittings along the fibres on compact principal torus bundle is topologically conjugate to map linear in fibres.

We clarify in which precise sense the theory of principal bundles and the theory of groupoids are equivalent; and how this equivalence of theories, in the differentiable case, reflects itself in the theory of connections. The method used is that of synthetic differential geometry. Introduction. In this note, we make explicit a sense in which the theory of principal fibre bundles is equivalent t...

It is known that the T-dual of a circle bundle with H-flux (given by a Neveu-Schwarz 3-form) is the T-dual circle bundle with dual H-flux. However, it is also known that torus bundles with H-flux do not necessarily have a T-dual which is a torus bundle. A big puzzle has been to explain these mysterious “missing T-duals.” Here we show that this problem is resolved using noncommutative topology. ...

By the gauge group bundle of a principal bundle P(B,G) we mean the Lie group bundle associated to P(B, G) through the conjugacy action of G on itself. Given only B and a Lie group bundle M on B, we ask if there exists P(B, G) with gauge group bundle isomorphic to M and, if so, how they can be described. Using a form of Whitehead’s concept of crossed module, in place of the idea of an ‘abstract ...

The topology of the non-adiabatic parameter space bundle is discussed for evolution of exact cyclic state vectors in Berry’s original example of split angular momentum eigenstates. It turns out that the change in topology occurs at a critical frequency. The first Chern number that classifies these bundles is proportional to angular momentum. The non-adiabatic principal bundle over the parameter...

Let X be a smooth projective curve defined over C whose genus is greater than one. We will generalize the Hitchin’s hamiltonian system to the cotangent bundle of the modular stack of principal SL2(C) bundle with parabolic reductions on X. Also its properties will be investigated. As an application, we will show a generalization of the Beilinson-Drinfeld isomorphism, which is a quantization of t...

A condition for determining the holonomy group associated to a principal bundle with connection is proven. Within the context of Holonomic Quantum Computation, this condition aids in determining the universality of the system. We apply the theory to the product bundle arising from the full two-qubit system of holonomic computation with squeezed coherent states and conclude that the control alge...