关于f-不变量的几何
On the geometry of the f-invariant
摘要：
f-不变量是e-不变量的更高版本，取值于模形式之间的可除同余;它可以被公式化为具有余维2的角的流形的椭圆亏格。在这篇论文中，我们发展了一个几何解释的f-不变的指标理论，从而提供了一个分析链接之间的稳定同伦群的球面和模形式的算术。特别是，我们能够建立一个公式，使我们能够计算f-不变从一个单一的脸。此外，我们将所得结果应用于笛卡儿积和主圆丛的情形，进行了显式计算。
英文摘要：
The f-invariant is a higher version of the e-invariant that takes values in the divided congruences between modular forms; it can be formulated as an elliptic genus of manifolds with corners of codimension two. In this thesis, we develop a geometrical interpretation of the f-invariant in terms of index theory, thereby providing an analytical link between the stable homotopy groups of the spheres and the arithmetic of modular forms. In particular, we are able to establish a formula that allows us to compute the f-invariant from a single face. Furthermore, we apply our results to the situation of cartesian products and principal circle bundles, performing explicit calculations.
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