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

Autor:	Nguyen, Minh Lam
Rok vydání:	2023
Předmět:	Mathematics - Geometric Topology Mathematics - Differential Geometry 57R57 53C27
Druh dokumentu:	Working Paper
Popis:	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. Comment: 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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2301.10245 Zobrazit plný text záznamu View this record from Arxiv