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
Department of Mathematics, Bates College, Lewiston 04240, ME, USA
Received 20 August 2003; Revised 9 February 2004
Copyright © 2004 Peter Wong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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)=∅.