# Coincidence free pairs of maps

Archivum Mathematicum (2006)

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

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topKoschorke, 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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