Rigidity of elliptic genera for non-spin manifolds

2022/12/02 by Michael Wiemeler, Wiemeler, Michael
Mathematics · #53C27 #57R15 #57R91 #57S15 #58J26 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2212.01059

openalex publication_date 2022/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the rigidity of elliptic genera for non-spin manifolds M with S¹-action. We show that if the universal covering of M is spin, then the universal elliptic genus of M is rigid. Moreover, we show that there is no condition which only depends on π₂(M) that guarantees the rigidity in the case that the universal covering of M is non-spin.

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