The Douady-Earle extension of quasihomographies

Douady-Earle section, holomorphic motions, and some applications

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.

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials

extension of the douady-hubbard's theorem on connectedness of the mandelbrot set to symmetric polynimials

Equivariant Dixmier-Douady Classes

An equivariant bundle gerbe à la Meinrenken over a G-manifold M is known to be a special type of S-gerbe over the differentiable stack [M/G]. We prove that the natural morphism relating the Cartan and simplicial models of equivariant cohomology in degree 3 maps the Dixmier-Douady class of an equivariant bundle gerbe à la Meinrenken to the Behrend-Xu-Dixmier-Douady class of the corresponding S-g...

Principal Bundles and the Dixmier Douady Class

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.