Numerical Computation of the Mapping Degree using Computational Homology

This paper describes numerical computation of the map- ping degree deg(f, Bd) for a continuous map f : Bd Rd on the d-dimensional ball Bd where d Z and 2. The mapping degree can be defined using a homomorphism which is induced on homology groups. We propose an effi- cient method to compute the homomorphism without direct calculation of homology groups, and obtain the mapping degree using computational homology.