Moduli Space for Invariant Solutions of Seiberg-Witten Equations

Year 2024, , 8 - 17, 27.05.2024

Muhiddin Uğuz

https://doi.org/10.29233/sdufeffd.1407647

Abstract

In this work we study the G-invariant solutions of the Seiberg-Witten equations when G is a cyclic group acting on a manifold M, preserving the metric and the orientation. G is assumed to have a lift to principle 〖Spin〗^c bundle which gives rise to Seiberg-Witten equations in question. In this work, we prove that when the dimension b_+^G of the G-fixed points of harmonic two forms is positive, for a generic choice of an element in this fixed point set, the moduli space of invariant solutions of Seiberg-Witten equations is a compact, smooth and oriented manifold of dimension d^G=ind D_A^G-b_+^G-1.

Keywords

Gauge Theory, Equivariant Seiberg-Witten theory, Equivariant Seiberg-Witten moduli space.

Ethical Statement

As the author of this study, I declare that I do not have any ethics committee approval and/or informed consent statement.

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