论文标题
拓扑Hecke特征形式
Topological Hecke eigenforms
论文作者
论文摘要
我们研究了A. Baker的Hecke操作员对各种拓扑空间的全态椭圆形同源性的作用的特征形式。对于某些类别的拓扑空间，我们证明了这些“拓扑Hecke eigenforms”空间的多种定理（即，这些“拓扑Hecke eigenforms”的一维性）对于某些类别的拓扑空间），我们给出了有限的CW-复合物的示例。我们还开发了一些摘要的“衍生的特征”，其激励例子是由于经典Hecke操作员未能通过Eisenstein系列乘以乘法的通勤。这一“衍生的特征”的一部分是对某些衍生的hecke特征形式的识别，是将拓扑Hecke特征形式从CW-复合物的顶部细胞扩展到其余CW-Complex的障碍物。使用这些障碍物类别与我们的多重性一个定理一起，我们用成对的经典模块化形式来明确计算拓扑hecke特征形式。
We study the eigenforms of the action of A. Baker's Hecke operators on the holomorphic elliptic homology of various topological spaces. We prove a multiplicity one theorem (i.e., one-dimensionality of the space of these "topological Hecke eigenforms" for any given eigencharacter) for some classes of topological spaces, and we give examples of finite CW-complexes for which multiplicity one fails. We also develop some abstract "derived eigentheory" whose motivating examples arise from the failure of classical Hecke operators to commute with multiplication by various Eisenstein series. Part of this "derived eigentheory" is an identification of certain derived Hecke eigenforms as the obstructions to extending topological Hecke eigenforms from the top cell of a CW-complex to the rest of the CW-complex. Using these obstruction classes together with our multiplicity one theorem, we calculate the topological Hecke eigenforms explicitly, in terms of pairs of classical modular forms, on all 2-cell CW complexes obtained by coning off an element in $π_n(S^m)$ which stably has Adams-Novikov filtration 1.
