相对陈character、边界和指数公式
Relative Chern character, boundaries and index formulae
摘要：
对于紧带边流形流形上具有几何K-理论的三类椭圆型伪微分算子，即Boutet de Monvel引入的“传递代数”、Mazzeo引入的“零代数”和[MR 95 k：58168]中的“散射代数”，我们给出了用Fredholm纤维算子族的符号（包括边界上的正规算子）表示的指标丛的Chern特征标的显式公式.这涉及到适当的描述，在每一种情况下，在一个有边界的带边流形上的向量丛的全空间的内部，紧支撑的上同调，其中陈特征标，从K-理论的相应实现映射，自然取值。
英文摘要：
For three classes of elliptic pseudodifferential operators on a compact manifold with boundary which have `geometric K-theory', namely the `transmission algebra' introduced by Boutet de Monvel, the `zero algebra' introduced by Mazzeo and the `scattering algebra' from [MR95k:58168] we give explicit formulae for the Chern character of the index bundle in terms of the symbols (including normal operators at the boundary) of a Fredholm family of fibre operators. This involves appropriate descriptions, in each case, of the cohomology with compact supports in the interior of the total space of a vector bundle over a manifold with boundary in which the Chern character, mapping from the corresponding realization of K-theory, naturally takes values.
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