publication

[eburroni@math.jussieu.fr]

A paper developping the 2 talks given by the authors at the CT2009 at  
Calais can now be found on line in arXiv under the title:

Elements for a metric tangential calculus,
by Elisabeth Burroni and Jacques Penon.

http://fr.arxiv.org/abs/0912.1012

Abstract:
The metric jets, introduced in the first chapter, generalize the jets  
(at order one) of Charles Ehresmann. In short, for a "good" map f  
(said to be "tangentiable" at a), we define its metric jet tangent at  
a (composed of all the maps which are locally lipschitzian at a and  
tangent to f at a) called the "tangential" of f at a, and denoted Tf_a  
(the domain and codomain of f being metric spaces).
Furthermore, guided by the heuristic example of the metric jet Tf_a,  
tangent to a map f differentiable at a, which can be canonically  
represented by the unique continuous affine map it contains, we will  
extend, in the second chapter, into a specific metric context, this  
property of representation of a metric jet.This yields a lot of  
relevant examples of such representations.

Happy new Year to all,

Elisabeth



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