Let X be a connected topological space and c∈H2(X;Z) non-zero cohomology class. A Homeo(X,c)-bundle is fiber bundle with whose structure group reduces to the Homeo(X,c) of c-preserving homeomorphisms X. If H1(X;Z)=0, then characteristic class for Homeo(X,c)-bundles called Dixmier-Douady defined via Serre spectral sequence. We show relation between universal foliated gauge extension Homeo(X,c). ...

Abstract Let $K$ denote either ${\mathbb{R}}$ or ${\mathbb{C}}$. In this article, we study two new equivariants and a invariant attached to rational map $f\in K(z)$ under the action of conjugation by ${\operatorname{SL}}_2(K)$. The 1st naturally live on real hyperbolic $[K:{\mathbb{Q}}]+1$ space carry information about $f$ ${\mathbb{P}}^1(K)$. When $K={\mathbb{C}}$, how these objects behave as ...

| We give a new proof that all external rays of the Man-delbrot set at rational angles land, and of the relation between the external angle of such a ray and the dynamics at the landing point. Our proof is diierent from the original one, given by Douady and Hubbard and reened by Lavaurs, in several ways: it replaces analytic arguments by combinatorial ones; it does not use complex analytic depe...

The non-associativity of translations in a quantum system with magnetic field background has received renewed interest association topologically trivial gerbes over $\mathbb{R}^n.$ is described by 3-cocycle the group $\mathbb{R}^n$ values unit circle $S^1.$ space $M$ are classified Dixmier-Douady class which an element $\mathrm{H}^3(M,\mathbb{Z}).$ However, there finer description terms local d...

We give a new proof that all external rays of the Mandelbrot set at rational angles land, and of the relation between the external angle of such a ray and the dynamics at the landing point. Our proof is different from the original one, given by Douady and Hubbard and refined by Lavaurs, in several ways: it replaces analytic arguments by combinatorial ones; it does not use complex analytic depen...

Examples of Fell algebras with compact spectrum and trivial Dixmier-Douady invariant are constructed to illustrate differences the case continuous-trace C ∗ <mml:annotation ...

Recently, Diaconescu, Moore and Witten provided a nontrivial link between K-theory and M-theory, by deriving the partition function of the Ramond-Ramond fields of Type IIA string theory from an E8 gauge theory in eleven dimensions. We give some relations between twisted K-theory and M-theory by adapting the method of [1], [2]. In particular, we construct the twisted K-theory torus which defines...

1.1. Mating: Definitions and some history. Mating quadratic polynomials is a topological construction suggested by Douady and Hubbard [Do2] to partially parametrize quadratic rational maps of the Riemann sphere by pairs of quadratic polynomials. Some results on matings of higher degree maps exist, but we will not discuss them in this paper. While there exist several, presumably equivalent, ways...