Rigidity of elliptic genera for non-spin manifolds
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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