Twisted Milnor Hypersurface I

Abstract

In this paper, we study {\bf twisted Milnor hypersurfaces} and compute their $\hat{A}$-genus and Atiyah-Singer-Milnor $\hat{I}\pm$-invariant. Our tool to compute the $\hat{I}\pm$-invariant is Zhang's analytic Rokhlin congruence formula. We also give some applications about group actions and metrics of positive scalar curvature on twisted Milnor hypersurfaces.