  We show the "non-existence" results are essential for all the previous known
applications of the Bauer-Furuta stable homotopy Seiberg-Witten invariants. As
an example, we present a unified proof of the adjunction inequalities.
  We also show that the nilpotency phenomenon explains why the Bauer-Furuta
stable homotopy Seiberg-Witten invariants are not enough to prove
11/8-conjecture.
