Fixed Point Theory and Applications
Volume 2004 (2004), Issue 2, Pages 89-95
doi:10.1155/S1687182004308107

Coincidence theory for spaces which fiber over a nilmanifold

Abstract

Let Y be a finite connected complex and p:Y→N a fibration over a compact nilmanifold N. For any finite complex X and maps f,g:X→Y, we show that the Nielsen coincidence number N(f,g) vanishes if the Reidemeister coincidence number R(pf,pg) is infinite. If, in addition, Y is a compact manifold and g is the constant map at a point a∈Y, then f is deformable to a map fˆ:X→Y such that fˆ−1(a)=∅.