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arXiv · 2412.02298

Topological Elliptic Genera I -- The mathematical foundation

Ying-Hsuan Lin·Mayuko Yamashita
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Abstract

We construct {\it Topological Elliptic Genera}, homotopy-theoretic refinements of the elliptic genera for $SU$-manifolds and variants including the Witten-Landweber-Ochanine genus. The codomains are genuinely $G$-equivariant Topological Modular Forms developed by Gepner-Meier, twisted by $G$-representations. As the first installment of a series of articles on Topological Elliptic Genera, this issue lays the mathematical foundation and discusses immediate applications. Most notably, we deduce an interesting divisibility result for the Euler numbers of $Sp$-manifolds.

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Ying-Hsuan Lin, Mayuko Yamashita. 2024-12-03. Topological Elliptic Genera I -- The mathematical foundation. https://arxiv.org/abs/2412.02298

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