Higher Spin Klein Surfaces

COVERS OF KLEIN SURFACES by

Higher Arf Functions and Topology of the Moduli Space of Higher Spin Riemann Surfaces

We describe all connected components of the space of pairs (P, s), where P is a hyperbolic Riemann surface with finitely generated fundamental group and s is an m-spin structure on P . We prove that any connected component is homeomorphic to a quotient of R by a discrete group. Our method is based on a description of an m-spin structure by an m-Arf function, that is a map σ : π1(P, p) → Z/mZ wi...

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, ...

Outline of Higher Igusa-klein Torsion

I will give an outline of the definition and basic properties of the version of higher Reidemeister torsion developed by John Klein and myself using parametrized Morse theory and polylogarithms. I also explain how this higher torsion is calculated first from the definition and from the axioms. I also explain at the end how these axioms might be extended to the case of nontrivial representations...

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 ...