Bounds on the fixed point indices for self-maps of certain simplicial complexes

This paper gives a generalization of results concerning fixed point index bounds for self-mappings of surfaces with boundary. Consider the class of finite polyhedra which have no local separating points and are homotopy equivalent to a one-complex. Given a member X of this class and a fixed point minimal self-mapping f :X→X it is shown that the index of each fixed point is bounded above by 1 , and also that for any collection of those with index less than −1 their total index is bounded below by 2χ−N , where N denotes the number of fixed points in the collection.