We introduce a cohomological invariant arising from a class in nonabelian cohomology. This invariant generalizes the Dixmier-Douady class and encodes the obstruction to a C*-algebra bundle being the fixed-point algebra of a gauge action. As an application, the duality breaking for group bundles vs. tensor C*-categories with non-simple unit is discussed in the setting of Nistor-Troitsky gauge-eq...

For polynomials, local connectivity of Julia sets is a much-studied and important property. Indeed, when the set polynomial degree $d\geq 2$ locally connected, topological dynamics can be completely described as quotient much simpler system: angle $d$-tupling on circle. transcendental entire function, less significant, but we may still ask for description system. To this end, introduce notion "...

We introduce differentiable stacks and explain the relationship with Lie groupoids. Then we study S-bundles and S-gerbes over differentiable stacks. In particular, we establish the relationship between S-gerbes and groupoid S-central extensions. We define connections and curvings for groupoid S-central extensions extending the corresponding notions of Brylinski, Hitchin and Murray for S-gerbes ...

For a finite rank projective bundle over a compact manifold, so associated to a torsion, Dixmier-Douady, 3-class, w, on the manifold, we define the ring of differential operators ‘acting on sections of the bundle’ in a formal sense. In particular any oriented even-dimensional manifold carries a projective spin Dirac operator in this sense. More generally the corresponding space of pseudodiffere...

The external argument theory of Douady and Hubbard allows us to know both the potential and the field-lines in the exterior of the Mandelbrot set. Nonetheless, there are no explicit formulae to operate with external arguments, and the external argument theory is difficult to apply. In this paper we introduce some tools in order to obtain formulae to operate with external arguments in the Mandel...

The reduction of the E8 gauge theory to ten dimensions leads to a loop group, which in relation to twisted K-theory has a Dixmier-Douady class identified with the Neveu-Schwarz H-field. We give an interpretation of the degree two part of the etaform by comparing the adiabatic limit of the eta invariant with the one loop term in type IIA. More generally, starting with a G-bundle, the comparison ...

Let M be a compact complex manifold equipped with a hyperkähler metric, and X be a closed complex analytic subvariety of M. In alg-geom 9403006, we proved that X is trianalytic (i. e., complex analytic with respect to all complex structures induced by the hyperkähler structure), provided that M is generic in its deformation class. Here we study the complex analytic deformations of trian-alytic ...

Let M be a compact complex manifold equipped with a hyperkk ahler metric, and X be a closed complex analytic subvariety of M. In alg-geom 9403006, we proved that X is trianalytic (i. e., complex analytic with respect to all complex structures induced by the hyperkk ahler structure), provided that M is generic in its deformation class. Here we study the complex analytic deformations of trian-aly...

We apply the $C^*$-algebraic formalism of topological T-duality due to Mathai and Rosenberg a broad class spaces that include torus bundles appearing in string theory compactifications with duality twists, such as nilmanifolds, well many other examples. develop simple procedure this setting for constructing T-duals starting from commutative $C^*$-algebra an action ${\mathbb R}^n$. treat general...