Moduli Space for Invariant Solutions of Seiberg-Witten Equations

Authors : Muhiddin Uğuz

Pages : 8-17

Doi:10.29233/sdufeffd.1407647

View : 40 | Download : 27

Publication Date : 2024-05-27

Article Type : Research Paper

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