Let D(M,N) be the set of all possible mapping degree from M to N, M1#M2 the connected sum of M1 and M2.
If D(M1,N) and D(M2,N) (resp. D(N,M1) & D(N,M2)) are already known, can D(M1#M2,N) (resp. D(N,M1#M2)) be calculated? Here all manifolds are assumed of dim >= 3.