Infinitesimal deformation of Deligne cycle class map

Infinitesimal deformation quantization of complex analytic spaces

For the physical aspects of deformation quantization we refer to the expository and survey papers [4] and [10]. Our objective is to initiate a version of global theory of quantization deformation in the category of complex analytic spaces in the same lines as the theory of (commutative) deformation. The goal of inifinitesimal theory is to do few steps towards construction of a star-product in t...

MAT 614 Notes on Infinitesimal Deformation Theory

For every local ring R in what follows, mR denotes the maximal ideal. Let Λ̃ be a complete, regular, local Noetherian ring, let E ⊂ m Λ̃ be an ideal, and denote the quotient by Λ. Thus, Λ is also a complete, local Noetherian ring. Denote the residue field Λ/mΛ by k. Denote by C = CΛ the category whose objects are Λ-algebras A such that (i) A is a local, Artin ring with mΛA ⊂ mA, and (ii) the indu...

EXPONENTIAL MAP OF A CLASS OF TOP SPACES

Class of the Infinitesimal Generator of a Diffeomorphism

Let F be an analytic diffeomorphism in (C m , 0) tangent to the identity of order n. The infinitesimal generator of F is the formal vector field X such that Exp X = F. In this paper we provide an elementary proof of the fact that X belongs to the Gevrey class of order 1/n.

Higher order infinitesimal bending of a class of toroids

In this paper we consider higher order infinitesimal bending of a surface in E3. Sufficient condition for a toroid generated by polygonal meridian to be non-rigid of higher order is given. This work is an extension of the results [1]-[7]. Examples of non-rigid surfaces, with visual presentation of infinitesimal bending are given. AMS Subj. Class.: 53A05, 53C45, 68U05