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Enriched Riemann sphere, Morse stability and equi‐singularity in 𝒪 2
Author(s) -
Kuo Tzee-Char,
Paunescu Laurentiu
Publication year - 2012
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdr049
Subject(s) - riemann sphere , mathematics , morse code , infinitesimal , pure mathematics , singularity , stability (learning theory) , mathematical analysis , riemann surface , computer science , telecommunications , machine learning
The Enriched Riemann Sphere ℂ P * 1 is ℂ P 1 plus a set of infinitesimals , having coordinates in the Newton–Puiseux field . Complex analysis is extended to the ‐ analysis ( Newton–Puiseux Analysis ). The classical Morse Stability Theorem is also extended; the stability idea is used to formulate an equi‐singular deformation theorem in ℂ{ x, y } (= 2 ).