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arXiv · 2112.01192

The complex genera, symmetric functions and multiple zeta values

Ping Li
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Abstract

We examine the coefficients in front of Chern numbers for complex genera, and pay special attention to the $\text{Td}^{\frac{1}{2}}$-genus, the $\Gamma$-genus as well as the Todd genus. Some related geometric applications to hyper-K\"{a}hler and Calabi-Yau manifolds are discussed. Along this line and building on the work of Doubilet in 1970s, various Hoffman-type formulas for multiple-(star) zeta values and transition matrices among canonical bases of the ring of symmetric functions can be uniformly treated in a more general framework.

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Ping Li. 2021-12-02. The complex genera, symmetric functions and multiple zeta values. https://doi.org/10.1016/j.jcta.2024.105893

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