The Seiberg-Witten equations for multiple-spinors on $4-$manifolds with definite intersection forms
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.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2023
- DOI:
- arXiv:
- arXiv:2301.10245
- Bibcode:
- 2023arXiv230110245N
- Keywords:
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- Mathematics - Geometric Topology;
- Mathematics - Differential Geometry;
- 57R57;
- 53C27
- E-Print:
- 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