S^2twistS^1:  (1, 1, 0 + Z_2, 0)
S^2xS^1:      (1, 1, 1, 1)
RP^2xS^1:     (1, 1 + Z_2, 0 + Z_2, 0)
RP^3#RP^3:    (1, 0 + Z_2^2, 0, 1)