Geodesic
Coincidence free pairs of maps
Archivum mathematicum, Tome 42 (2006) no. 5, pp. 105-117.

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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.
Classification : 55M20, 55Q52, 57R22
Keywords: coincidence; Nielsen number; minimum number; configuration space; projective space; filtration 
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     author = {Koschorke, Ulrich},
     title = {Coincidence free pairs of maps},
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     url = {http://geodesic.mathdoc.fr/item/ARM_2006__42_5_a2/}
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Koschorke, Ulrich. Coincidence free pairs of maps. Archivum mathematicum, Tome 42 (2006) no. 5, pp. 105-117. http://geodesic.mathdoc.fr/item/ARM_2006__42_5_a2/