In this letter we investigate some aspects of the noncommutative differential geometry based on derivations of the algebra of endomorphisms of an oriented complex hermitian vector bundle. We relate it, in a natural way, to the geometry of the underlying principal bundle and compute the cohomology of its complex of noncommutative differential forms. L.P.T.H.E.-ORSAY 98/14 Laboratoire associé au ...

A constructive approach to differential calculus on quantum principal bundles is presented. The calculus on the bundle is built in an intrinsic manner, starting from given graded (differential) *-algebras representing horizontal forms on the bundle and differential forms on the base manifold, together with a family of antiderivations acting on horizontal forms, playing the role of covariant der...

A gauge group is the topological of automorphisms a principal bundle. We compute integral cohomology ring classifying spaces groups U(n)-bundles over 2-sphere by generalizing operation for free loop spaces, called double suspension.

The bigerbes introduced here give a refinement of the notion 2-gerbes, representing degree four integral cohomology classes space. Defined in terms bisimplicial line bundles, have symmetry with respect to which they form 'bundle 2-gerbes' two ways; this structure replaces higher associativity conditions. We provide natural examples, including Brylinski-McLaughlin bigerbe associated principal G-...

We introduce the relative tail pressure to establish a variational principle for continuous bundle random dynamical systems. We also show that the relative tail pressure is conserved by the principal extension.

We describe how to obtain the imprimitivity bimodules of the noncommutative torus from a “principal bundle” construction, where the total space is a quasi-associative deformation of a 3-dimensional Heisenberg manifold.

BACKGROUND Central line-associated bloodstream infections (CLABSI) represent a serious patient safety issue. To prevent these infections, bundled interventions are increasingly recommended. We examine the extent of adoption of Central Line (CL) Bundle elements throughout US intensive care units (ICU) and determine their effectiveness in preventing CLABSIs. METHODOLOGY/PRINCIPAL FINDINGS In th...

We discuss a general procedure for using characteristic classes to study the components of the gauge group for a principal G-bundle. To illustrate this, we work out the case where G is the projective unitary group.

We define a quantum generalization of the algebra of functions over an associated vector bundle of a principal bundle. Here the role of a quantum principal bundle is played by a Hopf-Galois extension. Smash products of an algebra times a Hopf algebra H are particular instances of these extensions, and in these cases we are able to define a differential calculus over their associated vector bund...