The following problem is
studied: If points ck of a polyhedron and integers ik are given, when does there exist
a selfmap within a given homotopy class which has the ck as its fixed points and the
ik as its fixed point indices? Necessary and sufficient conditions for the existence of
such selfmaps are established if the selfmap is a deformation and the polyhedron is of
type W, and if the selfmap is arbitrary and the polyhedron is of type S. It is further
shown that there always exists a selfmap of an n-sphere (n ≧ 2) which has arbitrarily
prescribed locations and indices of its fixed points. The proofs are based on
Shi Gen-Hua’s construction of selfmaps with a minimum number of fixed
points.
