English

Enriched Riemann Sphere, Morse Stability and Equi-singularity in $\mathcal{O}_2$

Algebraic Geometry 2009-07-02 v1

Abstract

The \textit{Enriched Riemann Sphere} \CP1\C P_*^1 is \CP1\C P^1 plus a set of \textit{infinitesimals}, having the Newton-Puiseux field \F\F as coordinates. Complex Analysis is extended to the \F\F-\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 \C{x,y}(=O2)\C\{x,y\}(=\mathcal{O}_2).

Keywords

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

R2 v1 2026-06-21T13:19:59.289Z