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UID:6178@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20220127T140000
DTEND;TZID=Europe/Paris:20220127T150000
DTSTAMP:20250118T132857Z
URL:https://www.i2m.univ-amu.fr/evenements/on-approximation-of-maps-into-r
 eal-algebraic-homogeneous-spaces/
SUMMARY:Wojciech KUCHARZ (Uniwersytet Jagielloński\, Kraków): On approxim
 ation of maps into real algebraic homogeneous spaces
DESCRIPTION:Wojciech KUCHARZ: I will talk about a joint paper with Jacek Bo
 chnak containing an appendix written by János Kollár. Let X be a real al
 gebraic variety and let Y be a homogeneous space for some linear real alge
 braic group. We prove that a continuous map f: X --&gt\; Y can be approxim
 ated by regular maps in the compact-open topology if and only if it is hom
 otopic to a regular map. Taking Y to be the unit p-dimensional sphere\, we
  obtain solutions of several problems that have been open since the 1980's
  and which concern approximation of maps with values in the unit spheres. 
 This has several consequences for approximation of maps between unit spher
 es. For example\, we prove that for every positive integer n every continu
 ous map from the n-dimensional sphere into itself can be approximated by r
 egular maps. Up to now such a result has only been known for five special 
 values of n\, namely\, n=1\, 2\, 3\, 4 or 7.\n\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 021/10/Wojciech_Kucharz.jpg
CATEGORIES:Groupe de travail,Singularités,Virtual event
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DTSTART:20211031T020000
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