We extend previous results on boundedness of sets coherent sheaves a compact K\"ahler manifold to the relative and not necessarily smooth case. This enlarged context allows us prove properness properties Douady space as well related semistability such existence Harder-Narasimhan filtrations.

We review several applications of Douady-Earle section to holomorphic motions over infinite dimensional parameter spaces. Using DouadyEarle section we study group-equivariant extensions of holomorphic motions. We also discuss the relationship between extending holomorphic motions and lifting holomorphic maps. Finally, we discuss several applications of holomorphic motions in complex analysis.

A systematic consideration of the problem of the reduction and extension of the structure group of a principal bundle is made and a variety of techniques in each case are explored and related to one another. We apply these to the study of the DixmierDouady class in various contexts including string structures, Ures bundles and other examples motivated by considerations from quantum field theory.

In this paper, we study rational functions of the form [Formula: see text] with fixed and at least text], hold either or while other varies. We locate some homeomorphic copies Mandelbrot set in text]-parameter plane for certain ranges as well text]-plane text]-ranges. use techniques first introduced by Douady Hubbard [1985] that were applied subfamily Devaney [2006]. These involve polynomial-li...

Using groupoid S-central extensions, we present, for a compact simple Lie group G, an infinite dimensional model of S-gerbe over the differential stack G/G whose Dixmier-Douady class corresponds to the canonical generator of the equivariant cohomology H G(G). c © 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS Gerbes Equivariantes sur les groupes de Lie simples compa...