Nilpotency of the Bauer-Furuta stable homotopy Seiberg-Witten invariants

TL;DR

This paper proves a nilpotency theorem for the Bauer-Furuta stable homotopy Seiberg-Witten invariants in certain smooth 4-manifolds, advancing understanding of their algebraic properties.

Contribution

It establishes a nilpotency result for these invariants in smooth closed 4-manifolds with trivial first Betti number, a novel theoretical insight.

Findings

Proves nilpotency of the invariants under specified conditions

Provides new algebraic constraints on Seiberg-Witten invariants

Enhances theoretical understanding of 4-manifold invariants

Abstract

We prove a nilpotency theorem for the Bauer-Furuta stable homotopy Seiberg-Witten invariants for smooth closed 4-manifolds with trivial first Betti number.