The Seiberg-Witten equations for multiple-spinors on $4-$manifolds with definite intersection forms
Geometric Topology
2023-01-30 v2 Differential Geometry
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.
Cite
@article{arxiv.2301.10245,
title = {The Seiberg-Witten equations for multiple-spinors on $4-$manifolds with definite intersection forms},
author = {Minh Lam Nguyen},
journal= {arXiv preprint arXiv:2301.10245},
year = {2023}
}
Comments
The proof of the theorem in the notes relies on the results stated in our other posting arXiv:2301.09693. Specifically, one of the ingredients needed is transversality. It is pointed out to us that due to a technicality in our set-up, the system of equations that we consider is not elliptic. Hence, we should not expect transversality in this set-up