Numerical Computation of the Mapping Degree using Computational Homology

This paper describes numerical computation of the mapping degree deg(f, B^d)for a continuous map f : B^d) R^d on the d-dimensional ball B^d 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.