Just asC principal bundles provide a geometric realisation of two-dimensional integral cohomology; gerbes or sheaves of groupoids, provide a geometric realisation of three dimensional integral cohomology through their Dixmier-Douady class. I consider an alternative, related, geometric realisation of three dimensional cohomology called a bundle gerbe. Every bundle gerbe gives rise to a gerbe and...

Barchans are dunes of high mobility which have a crescent shape and propagate under conditions of unidirectional wind. However, sand dunes only appear above a critical size, which scales with the saturation distance of the sand flux [P. Hersen, S. Douady, and B. Andreotti, Phys. Rev. Lett. 89, 264301 (2002); B. Andreotti, P. Claudin, and S. Douady, Eur. Phys. J. B 28, 321 (2002); G. Sauermann, ...

We show that there exists an entire function without finite asymp-totic values for which the associated Newton function tends to infinity in some invariant domain. The question whether such a function exists had been raised by Douady.

We show that transgression of the Dixmier-Douady class coming from the natural gerbe arising in the discussion of Faddeev's anomaly is the Faddeev-Mickelsson two cocycle.

We continue the description of Mandelbrot and Multibrot sets and of Julia sets in terms of fibers which was begun in [S3] and [S4]. The question of local connectivity of these sets is discussed in terms of fibers and becomes the question of triviality of fibers. In this paper, the focus is on the behavior of fibers under renormalization and other surgery procedures. We show that triviality of f...

In the preceding two papers (1, 2) we have described aberrant strains of rabbit fibroma virus, a virus which normally gives rise to fibroma-like growths at the site of inoculation in cottontail or domestic rabbits (3). Those chiefly studied were derived from a growth in one cottontail rabbit (A); the strain in its original form is designated "original fibroma virus," fibromatous virus or OA str...

We prove that every bounded type Siegel disk of a rational map must be a quasi-disk with at least one critical point on its boundary. This verifies Douady-Sullivan’s conjecture in the case of bounded type rotation numbers.

with a xed point of multiplier = e 2 i at the origin. Take to be real and irrational. For generic choice of (in the sense of Baire category), Cremer showed that there is no local linearizing coordinate near the origin. We will say brie y that the origin is a Cremer point, or that P is a Cremer polynomial . According to Sullivan and Douady, the existence of such a Cremer point implies that the J...