An algorithmic approach to the construction of homomorphisms induced by maps in homology
Madjid Állili, Tomasz Kaczyński · Transactions of the American Mathematical Society · 1999
This paper is devoted to giving the theoretical background for an algorithm for computing homomorphisms induced by maps in homology. The principal idea is to insert the graph of a given continuous map f \, f \, into a graph of a multi-valued representable map F \, F . The multi-valued representable maps have well developed continuity properties and admit a finite coding that permits treating them by combinatorial methods. We provide the construction of the homomorphism F ∗ \, F_* \, induced by F \, F \, such that F ∗ = f ∗ \, F_* = f_* . The presented construction does not require subsequent barycentric subdivisions and simplicial approximations of f \, f . The main motivation for this paper comes from the project of computing the Conley Index for discrete dynamical systems.