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UID:7208@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20220127T140000
DTEND;TZID=Europe/Paris:20220127T150000
DTSTAMP:20220121T090441Z
URL:https://www.i2m.univ-amu.fr/events/on-approximation-of-maps-into-real-
algebraic-homogeneous-spaces/
SUMMARY:On approximation of maps into real algebraic homogeneous spaces - W
ojciech KUCHARZ
DESCRIPTION:I will talk about a joint paper with Jacek Bochnak containing a
n appendix written by János Kollár. Let X be a real algebraic variety an
d let Y be a homogeneous space for some linear real algebraic group. We pr
ove that a continuous map f: X -->\; Y can be approximated by regular ma
ps in the compact-open topology if and only if it is homotopic to a regula
r 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 c
onsequences for approximation of maps between unit spheres. For example\,
we prove that for every positive integer n every continuous map from the n
-dimensional sphere into itself can be approximated by regular maps. Up to
now such a result has only been known for five special values of n\, name
ly\, 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:Séminaire Singularités,Virtual event
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TZID:Europe/Paris
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DTSTART:20211031T020000
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