Fredholm realizations of elliptic symbols on manifolds with boundary II: fibered boundary

Details Fredholm realizations of elliptic symbols on manifolds with boundary II: fibered boundary Fredholm realizations of elliptic symbols on manifolds with boundary II: fibered boundary

2009-05-04

arxiv.org/abs/0905.0453v2

Proceedings of "Motives, Quantum Field Theory, and Pseudodifferential Operators" at Boston University June 2-13, 2008

Mathematics

Differential Geometry

Scientific paper

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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