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arXiv · 2401.06944

SL(2,Z) modular forms and Witten genus in odd dimensions

Jianyun Guan·Yong Wang·Haiming Liu
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Abstract

By some SL(2, Z) modular forms introduced in [4] and [10], we construct some modular forms over SL2(Z) and some modular forms over {\Gamma}^0(2) and {\Gamma}_0(2) in odd dimensions. In parallel, we obtain some new cancellation formulas for odd dimensional spin manifolds and odd dimensional spin^c manifolds respectively. As corollaries, we get some divisibility results of index of the Toeplitz operators on spin manifolds and spin^c manifolds .

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Jianyun Guan, Yong Wang, Haiming Liu. 2024-01-13. SL(2,Z) modular forms and Witten genus in odd dimensions. https://arxiv.org/abs/2401.06944

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