On the existence of G-equivariant maps

Borsuk–Ulam theorems and their parametrized versions for spaces of type (a,b)

“…Further, via the induced homomorphism y , H . y E/ is an H .B/-module generated by (2) 1; a; a 2 ; : : : ; a 3n 1 ; a 3n ; c; ac; : : : ; a n c:…”

“…Let u i generate H i n .X I Z/, for i D 0; 1; 2 and 3. Then the structure of the Z-cohomology ring of X is determined by the two integers a and b for which u 2 1 D au 2 and u 1 u 2 D bu 3 . In this case, X is said to be of type .a; b/.…”