Todd genus and $A_k$-genus of unitary $S^1$-manifolds

Jianbo Wang; Yuyu Wang; Zhiwang Yu

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Todd genus and A_k-genus of unitary S¹-manifolds

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arxiv 2012.10908 v1 pith:HSQENIV6 submitted 2020-12-20 math.AT

Todd genus and A_k-genus of unitary S¹-manifolds

Jianbo Wang , Zhiwang Yu , Yuyu Wang This is my paper

classification math.AT

keywords genusclasscohomologyfirstintegraltoddunitaryaction

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Assume that $M$ is a compact connected unitary 2n-dimensional manifold and admits a non-trivial circle action preserving the given complex structure. If the first Chern class of $M$ equals to $k_0x$ for a certain 2nd integral cohomology class $x$ with $|k_0|\geq n + 2$, and its first integral cohomology group is zero, this short paper shows that the Todd genus and $A_k$-genus of $M$ vanish.

Todd genus and A_k-genus of unitary S¹-manifolds

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