The Seiberg-Witten equations for multiple-spinors on $4-$manifolds with definite intersection forms

TL;DR

This paper offers a new proof of Donaldson's Diagonalization Theorem using an abelian gauge-theoretic approach with multiple-spinor Seiberg-Witten equations, highlighting the role of Elkies' theorem.

Contribution

It introduces a novel abelian gauge-theoretic method for proving Donaldson's theorem, extending Seiberg-Witten theory to multiple-spinors.

Findings

Proof of Donaldson's Diagonalization Theorem via new gauge-theoretic approach

Extension of Seiberg-Witten equations to multiple-spinors on 4-manifolds

Demonstrates the role of Elkies' theorem in this context

Abstract

In this note, we present a proof of Donaldson's Diagonalization Theorem via an abelian gauge-theoretic variant of the Seiberg-Witten equations for multiple spinors. Like the other proof of Donaldson's theorem using the standard Seiberg-Witten theory, Elkies' theorem also plays a key role in our argument.