2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224759We 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.This is the version published by Geometry & Topology Monographs on 29 January 2007Algebraic Topology55P91, 55P92, 57R57, 55P42, 57M50text