Twisted Milnor Hypersurface I
Jingfang Lian, Fei Han, Hao Li, and Zhi L\"u
TL;DR
This paper investigates twisted Milnor hypersurfaces, computing their $ ext{A}$-genus and $ ext{alpha}$-invariant using Zhang's formula, and explores applications in group actions and positive scalar curvature metrics.
Contribution
It introduces the study of twisted Milnor hypersurfaces and applies Zhang's analytic Rokhlin congruence to compute their invariants, with new applications in geometry.
Findings
Computed $ ext{A}$-genus and $ ext{alpha}$-invariant for twisted Milnor hypersurfaces
Established applications to group actions on these hypersurfaces
Analyzed metrics of positive scalar curvature on the hypersurfaces
Abstract
In this paper, we study {\bf twisted Milnor hypersurfaces} and compute their -genus and Atiyah-Singer-Milnor -invariant. Our tool to compute the -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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory