On the Least Number of Fixed Points
Boju Jiang · American Journal of Mathematics · 1980
THEOREM ([8], see also [1], [3], and [6]). If X has no local separating points and dim X 2 3, then for any self-map f of X we have N(f) = M(f). Here by a local separating point we mean a point x E X at which H1(X, X x) ? 0, or, equivalently, at which there is a connected neighborhood U such that U x is not connected. For any triangulation K of X, X has no local separating points iff every maximal simplex of K is of dimension >2 and for every vertex v of K the boundary of stK v is connected. The purpose of this paper is to improve the above theorem.