Pure and Applied Mathematics Quarterly

Volume 18 (2022)

Number 3

Twisted Milnor hypersurfaces

Pages: 923 – 970

DOI: https://dx.doi.org/10.4310/PAMQ.2022.v18.n3.a4

Authors

Jingfang Lian (School of Mathematical Sciences, Fudan University, Shanghai, China)

Fei Han (Department of Mathematics, National University of Singapore)

Hao Li (National University of Singapore)

Zhi Lü (School of Mathematical Sciences, Fudan University, Shanghai, China)

Abstract

In this paper, we study twisted Milnor hypersurfaces and compute their $\widehat{A}$-genus and Atiyah–Singer–Milnor $\alpha$-invariant. Our tool to compute the $\alpha$-invariant is Zhang’s analytic Rokhlin congruence formula. We also give some applications about the geometry, more precisely, group actions and existence of Riemannian metrics of positive scalar curvature on twisted Milnor hypersurfaces.

Keywords

twisted Milnor hypersurface, $\widehat{A}$-genus, $\alpha$ invariant, positive scalar curvature

2010 Mathematics Subject Classification

14Q10, 19K56

Full Text (PDF format)

Jingfang Lian and Zhi Lü are partially supported by the grant from NSFC (No. 11971112); Fei Han is partially supported by the grant AcRF R-146- 000-218-112 from National University of Singapore; Hao Li is partially supported by the grant R-146-000-322-114 from National University of Singapore.

Received 16 December 2021

Received revised 20 January 2022

Accepted 4 February 2022

Published 24 July 2022