Enriched Riemann Sphere, Morse Stability and Equi-singularity in $\mathcal{O}_2$
Algebraic Geometry
2009-07-02 v1
Abstract
The \textit{Enriched Riemann Sphere} is plus a set of \textit{infinitesimals}, having the Newton-Puiseux field as coordinates. Complex Analysis is extended to the -\textit{Analysis} (\textit{Newton-Puiseux Analysis}). The classical \textit{Morse Stability Theorem} is also extended; the \textit{stability idea} is used to formulate an \textit{equi-singular deformation theorem} in .
Cite
@article{arxiv.0907.0105,
title = {Enriched Riemann Sphere, Morse Stability and Equi-singularity in $\mathcal{O}_2$},
author = {T. C. Kuo and L. Paunescu},
journal= {arXiv preprint arXiv:0907.0105},
year = {2009}
}
Comments
29 pages, 4 figures