On finite energy monopoles on $\mathbb{C}\times \Sigma$

DOI10.4310/CAG.2022.V30.N2.A5arXiv1811.03139MaRDI QIDQ6309375

Donghao Wang

Publication date: 7 November 2018

Abstract: Let $X=mathbbCimesSigma$ be the product of the complex plane and a compact Riemann surface. We establish a classification theorem of solutions to the Seiberg-Witten equation on $X$ with finite analytic energy. The spin bundle $S^{+}oX$ splits as $L^{+}oplus{L}^{-}$. When $2-2gleq{c}_1(S^{+})[Sigma]<0$, the moduli space is in bijection with the moduli space of pairs $$ where $$ is a holomorphic structure on $L^{+}$ and $$ is a polynomial map. Moreover, the solution has analytic energy $-4p{i}^{2}dcdot{c}_1(S^{+})[Sigma]$ if $f$ has degree $d$. When $c_1(S^{+})=0$, all solutions are reducible and the moduli space is the space of flat connections on $$. We also estimate the decay rate of these solutions at infinity.

Mathematics Subject Classification ID

Applications of global analysis to structures on manifolds (57R57) Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07)

This page was built for publication: On finite energy monopoles on $\mathbb{C}\times \Sigma$

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6309375)