几个新的双变量椭圆亏格
Several new two-variable elliptic genera
浏览论文内容
中文总结 AI 辅助
研究为偶数维自旋流形定义新双变量椭圆亏格，借助其与狄拉克算子及多种雅可比形式的关系得出\(SL(2,\mathbb{Z})\)和\(\Gamma^0(2)\)模形式，最终获得自旋流形的反常消去公式。
中文摘要 AI 辅助
本文为偶数维自旋流形定义了几个新的双变量椭圆亏格，它们是某些狄拉克算子和全纯\(SL(2,\mathbb{Z})\)、\(\Gamma_0(2)\)、\(\Gamma^0(2)\)、\(\Gamma_{\theta}\)-雅可比形式的指标。通过这些雅可比形式可得到一些\(SL(2,\mathbb{Z})\)和\(\Gamma^0(2)\)模形式，进而为自旋流形得到有趣的反常消去公式。
英文摘要
In this paper, we define several new two-variable elliptic genera for even dimensional spin manifolds which are the index for some Dirac operators and holomorphic $SL(2,Z)$, $Γ_0(2)$, $Γ^0(2)$, $Γ_θ$-Jacobi forms. By these Jacobi forms, we can get some $SL(2,{\bf Z})$ and $Γ^0(2)$ modular forms. By these $SL(2,{\bf Z})$ and $Γ^0(2)$ modular forms, we get some interesting anomaly cancellation formulas for spin manifolds.
