Fixed Point Theory and Applications
Volume 2006 (2006), Article ID 29470, 10 pages

Epsilon Nielsen fixed point theory

Robert F. Brown

Department of Mathematics, University of California, Los Angeles 90095-1555, CA, USA

Received 11 October 2004; Revised 17 May 2005; Accepted 21 July 2005

Copyright © 2006 Robert F. Brown. 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.


Let f:XX be a map of a compact, connected Riemannian manifold, with or without boundary. For >0 sufficiently small, we introduce an -Nielsen number N(f) that is a lower bound for the number of fixed points of all self-maps of X that are -homotopic to f. We prove that there is always a map g:XX that is -homotopic to f such that g has exactly N(f) fixed points. We describe procedures for calculating N(f) for maps of 1-manifolds.