Bounds on the fixed point indices for self-maps of certain simplicial complexes (Q1588334)

The main result of the paper under review (stated in Theorem 1.1) shows that, if \(X\) is a compact, connected polyhedron without any local separating points which is homotopy equivalent to a one-complex and \(f:X\to Y\) is a fixed-point minimal self-mapping, then for each fixed point \(p\) of \(f\), its index is bounded above by \(1\), and also the total index of all fixed points whose index is less than or equal to \(-1\), is bounded below by \(2\chi(X)-N\), where \(\chi(X)\) denotes the Euler characteristic of X and \(N\) denotes the number of all fixed points considered.