RELATIVE CHERN CHARACTER, BOUNDARIES AND INDEX FORMULAS
RELATIVE CHERN CHARACTER, BOUNDARIES AND INDEX FORMULAS
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相对陈的特征、边界和指数公式
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
R. Melrose
中科院分区：
文献类型：
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作者：
Pierre Albin;R. Melrose
对于紧致流形上具有“几何K-理论”的三类椭圆型伪微分算子，即Boutet de Monvel [5]引入的“传递代数”、Mazzeo [9，10]引入的“零代数”和[16]引入的“散射代数”，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，在一个流形上的向量丛的全空间的内部的紧支撑的上同调，其中的陈特征标，映射从相应的实现K-理论，自然取值。
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 [5], the "zero algebra" introduced by Mazzeo in [9, 10] and the "scattering algebra" from [16], we give explicit formulas for the Chern character of the index bundle in terms of the symbols (including normal operators at the boundary) of a Fredholm family of fiber 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.