CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Approximation and the Topology of Rationally Convex Sets

  Published:2006-12-01
 Printed: Dec 2006
  • E. S. Zeron
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

Considering a mapping $g$ holomorphic on a neighbourhood of a rationally convex set $K\subset\cc^n$, and range into the complex projective space $\cc\pp^m$, the main objective of this paper is to show that we can uniformly approximate $g$ on $K$ by rational mappings defined from $\cc^n$ into $\cc\pp^m$. We only need to ask that the second \v{C}ech cohomology group $\check{H}^2(K,\zz)$ vanishes.
Keywords: Rationally convex, cohomology, homotopy Rationally convex, cohomology, homotopy
MSC Classifications: 32E30, 32Q55 show english descriptions Holomorphic and polynomial approximation, Runge pairs, interpolation
Topological aspects of complex manifolds
32E30 - Holomorphic and polynomial approximation, Runge pairs, interpolation
32Q55 - Topological aspects of complex manifolds
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/