Numerical Computation of the Mapping Degree using Computational Homology

Abstract

This paper describes numerical computation of the mapping degree deg(f, Bd)for a continuous map f : Bd) Rd on the d-dimensional ball Bd where d isin Z and ges2. The mapping degree can be defined using a homomorphism which is induced on homology groups. We propose an efficient method to compute the homomorphism without direct calculation of homology groups, and obtain the mapping degree using computational homology.