I am not impressed by any authority or fashion arguments, my question is the following: is there somebody who said interesting mathematical things about this work?
I put on arxiv two papers
- Maps of metric spaces which is the slightly edited appendix of Computing with space
- Normed groupoids with dilations which is an improved version of Deformations of normed groupoids
The paper Computing with space contains too may ideas, is too dense, therefore much of it will not be read, as I was warned repeatedly. This is the reason to do again what I did with Introduction to metric spaces with dilations, which is a slightly edited part of the paper A characterization of sub-riemannian spaces as length dilation structures. Apparently the part (Introduction to ..), the small detail, is much more read than the whole (A characterization…).
Concerning the second paper “Normed groupoids…”, it is an improvement of the older paper. Why did I not updated the older paper? Because I need help, I just don’t understand where this is going (and why such direction of research was not explored before).
Until recently, on my home page was a link to the scan of the paper
which is no longer visible now. But maybe it deserves a post here, because is my oldest attempt to understand differential calculus as an abstract matter and to look to new forms of it.
To me it became clear that differential calculus admits variants, in the same spirit as euclidean geometry admitting non-euclidean variants. At that moment I had no really intersting examples of such a “non-euclidean” differential calculus, so I switched to other research subjects. Nobody pointed to me the huge paper
Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un, The Annals of Mathematics Second Series, Vol. 129, No. 1 (Jan., 1989), pp. 1-60
by Pierre Pansu. It was only luck that in 2000, at Lausanne, I met Sergey Vodop’yanov (from Sobolev Institute of Mathematics). He started to explain to me what Carnot groups are and I was thrilled to learn that examples I needed previously are numerous in sub-riemannian geometry.
With the right frame of mind (at least I think so), that of intrinsic dilations, I started then to study sub-riemannian geometry.