A Van Kampen type theorem for coincidences

✍ Scribed by L.D. Borsari; D.L. Gonçalves

• Book ID: 104295523
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 157 KB
• Volume: 101
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(98)00115-1

✦ Synopsis

The Nielsen coincidence theory is well understood for a pair of maps (f, g) : M n → N n where M and N are compact manifolds of the same dimension greater than two. We consider coincidence theory of a pair (f, g) : K → N n , where the complex K is the union of two compact manifolds of the same dimension as N n . We define a number N(f, g : K 1 , K 2 ) which is a homotopy invariant with respect to the maps. This number is certainly a lower bound for the number of coincidence points, and we prove a minimizing theorem with respect to this number. Finally, we consider the case where the target is a Jiang space and we obtain a nicer description of N(f, g : K 1 , K 2 ) in terms of the Nielsen coincidence numbers of the maps restricted to the subspaces K 1 , K 2 .