DOUBLES OF KLEIN SURFACES

COVERS OF KLEIN SURFACES by

Dynamics of Dianalytic Transformations of Klein Surfaces

This paper is an introduction to dynamics of dianalytic self-maps of nonorientable Klein surfaces. The main theorem asserts that dianalytic dynamics on Klein surfaces can be canonically reduced to dynamics of some classes of analytic self-maps on their orientable double covers. A complete list of those maps is given in the case where the respective Klein surfaces are the real projective plane, ...

Hochschild Homology and Cohomology of Klein Surfaces

Within the framework of deformation quantization, a first step towards the study of star-products is the calculation of Hochschild cohomology. The aim of this article is precisely to determine the Hochschild homology and cohomology in two cases of algebraic varieties. On the one hand, we consider singular curves of the plane; here we recover, in a different way, a result proved by Fronsdal and ...

Quantization of Drinfel’d doubles

Hopf algebra quantizations of 4-dimensional and 6-dimensional real classical Drinfel’d doubles are studied by following a direct “analytic” approach. The full quantization is explicitly obtained for most of the Drinfel’d doubles, except a small number of them for which the dual Lie algebra is either sl2 or so(3). In the latter cases, the classical r-matrices underlying the Drinfel’d double quan...

Shared delusions of doubles.

This is the first report of two partners in a folie à deux situation manifesting identical Capgras delusions. It is postulated that the Capgras syndrome developed as a result of interaction between a dominant patient with primarily paranoid psychopathology and a submissive one with primarily organic dysfunction. The submissive "neuro-organic" partner experienced a non-delusional misidentificati...