论文标题
与离散的分离组的作用相关的非局部椭圆问题
Nonlocal elliptic problems associated with actions of discrete groups on manifolds with boundary
论文作者
论文摘要
给定具有离散基团在其上的作用的边界的歧管，我们考虑了pseudodivfientence边界值问题的元素生成的运算符代数，以及在歧管及其边界上作用在函数上的转移操作员。在小组动作的某些条件下，我们为该代数中的椭圆形元素的符号构建了一个Chern特征，其值是固定点歧管的DE RHAM类型的共同体，并根据此Chern特征获得索引公式。
Given a manifold with boundary endowed with an action of a discrete group on it, we consider the algebra of operators generated by elements in the Boutet de Monvel algebra of pseudodifferential boundary value problems and shift operators acting on functions on the manifold and its boundary. Under certain conditions on the group action, we construct a Chern character for symbols of elliptic elements in this algebra with values in a de Rham type cohomology of the fixed point manifolds and obtain an index formula in terms of this Chern character.
