具有纤维边界的流形上椭圆符号的Fredholm实现II：纤维边界
Fredholm realizations of elliptic symbols on manifolds with boundary II: fibered boundary
摘要：
我们考虑两个演算的伪微分算子的纤维边界流形上：Mazzeo的边缘演算，其中有作为本地模型的运营商与封闭流形的产品渐近双曲空间，和phi演算的Mazzeo和第二作者，这是类似的产品上的闭流形与渐近欧几里得空间。我们构建了一个绝热演算的运营商之间的插值，并使用它来计算'光滑' K-理论群的边缘演算，确定存在的Fredholm量子化的椭圆符号，并建立一个家庭的指标定理在K-理论。
英文摘要：
We consider two calculi of pseudodifferential operators on manifolds with fibered boundary: Mazzeo's edge calculus, which has as local model the operators associated to products of closed manifolds with asymptotically hyperbolic spaces, and the phi calculus of Mazzeo and the second author, which is similarly modeled on products of closed manifolds with asymptotically Euclidean spaces. We construct an adiabatic calculus of operators interpolating between them, and use this to compute the `smooth' K-theory groups of the edge calculus, determine the existence of Fredholm quantizations of elliptic symbols, and establish a families index theorem in K-theory.
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