# Enriched Riemann Sphere, Morse Stability and Equi-singularity in $mathcal{O} 2$ - Mathematics > Algebraic Geometry

Enriched Riemann Sphere, Morse Stability and Equi-singularity in $mathcal{O} 2$ - Mathematics > Algebraic Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: The \textit{Enriched Riemann Sphere} $\C P *^1$ is $\C P^1$ plus a set of\textit{infinitesimals}, having the Newton-Puiseux field $\F$ as coordinates.Complex Analysis is extended to the $\F$-\textit{Analysis}\textit{Newton-Puiseux Analysis}. The classical \textit{Morse StabilityTheorem} is also extended; the \textit{stability idea} is used to formulate an\textit{equi-singular deformation theorem} in $\C\{x,y\}=\mathcal{O} 2$.

Author: T.C. Kuo, L. Paunescu

Source: https://arxiv.org/