singular homological degree as group epimorphism

by singular homological degree of the identity on the sphere we get

consider

for as pinch map of circles Since reduced singular homology and wedge product, we get

Here is the diagonal map (?), thus the composition is given by

Taking this results in

resp. by iteration

follows from:

• singular homological degree of a reflection
• multiplicativity of the singular homological degree on the sphere
• singular homological degree of a nullhomotopic map on the sphere