Coincidence free pairs of maps

Ulrich Koschorke

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 5, page 105-117
  • ISSN: 0044-8753

Abstract

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This paper centers around two basic problems of topological coincidence theory. First, try to measure (with the help of Nielsen and minimum numbers) how far a given pair of maps is from being loose, i.e. from being homotopic to a pair of coincidence free maps. Secondly, describe the set of loose pairs of homotopy classes. We give a brief (and necessarily very incomplete) survey of some old and new advances concerning the first problem. Then we attack the second problem mainly in the setting of homotopy groups. This leads also to a very natural filtration of all homotopy sets. Explicit calculations are carried out for maps into spheres and projective spaces.

How to cite

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Koschorke, Ulrich. "Coincidence free pairs of maps." Archivum Mathematicum 042.5 (2006): 105-117. <http://eudml.org/doc/249811>.

@article{Koschorke2006,
abstract = {This paper centers around two basic problems of topological coincidence theory. First, try to measure (with the help of Nielsen and minimum numbers) how far a given pair of maps is from being loose, i.e. from being homotopic to a pair of coincidence free maps. Secondly, describe the set of loose pairs of homotopy classes. We give a brief (and necessarily very incomplete) survey of some old and new advances concerning the first problem. Then we attack the second problem mainly in the setting of homotopy groups. This leads also to a very natural filtration of all homotopy sets. Explicit calculations are carried out for maps into spheres and projective spaces.},
author = {Koschorke, Ulrich},
journal = {Archivum Mathematicum},
keywords = {coincidence; Nielsen number; minimum number; configuration space; projective space; filtration; coincidence; Nielsen number; minimum number; configuration space; projective space; filtration},
language = {eng},
number = {5},
pages = {105-117},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Coincidence free pairs of maps},
url = {http://eudml.org/doc/249811},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Koschorke, Ulrich
TI - Coincidence free pairs of maps
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 5
SP - 105
EP - 117
AB - This paper centers around two basic problems of topological coincidence theory. First, try to measure (with the help of Nielsen and minimum numbers) how far a given pair of maps is from being loose, i.e. from being homotopic to a pair of coincidence free maps. Secondly, describe the set of loose pairs of homotopy classes. We give a brief (and necessarily very incomplete) survey of some old and new advances concerning the first problem. Then we attack the second problem mainly in the setting of homotopy groups. This leads also to a very natural filtration of all homotopy sets. Explicit calculations are carried out for maps into spheres and projective spaces.
LA - eng
KW - coincidence; Nielsen number; minimum number; configuration space; projective space; filtration; coincidence; Nielsen number; minimum number; configuration space; projective space; filtration
UR - http://eudml.org/doc/249811
ER -

References

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