标题： 拓扑椭圆指标 I -- 数学基础 显示英文标题

标题： Topological Elliptic Genera I -- The mathematical foundation

摘要： 我们构造了{\it 拓扑椭圆指标}，即$SU$-流形及其变体（包括 Witten-Landweber-Ochanine 亏格）的同伦理论精化。 陪域是 Gepner-Meier 开发的真正$G$-等变拓扑模形式，由$G$-表示进行扭曲。 作为一系列关于拓扑椭圆亏格文章的第一部分，本文建立了数学基础并讨论了直接应用。 最显著的是，我们推导出$Sp$-流形的欧拉数的一个有趣可除性结果。 显示英文摘要

摘要： 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.