O2 (C)-Vector Bundles and Equivariant Real Circle Actions

Abstract : The main goal of this article is to give an expository overview of some new results on real circle actions on affine four-space and their relation to previous results on O2(C)-equivariant vector bundles. In Moser-Jauslin (Infinite families of inequivalent real circle actions on affine four-space, 2019, [13]), we described infinite families of equivariant real circle actions on affine four-space. In the present note, we will describe how these examples were constructed, and some consequences of these results.