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

Author(s)
Albin, Pierre; Melrose, Richard B.
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Abstract
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 φ 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.
Date issued
2010-01
URI
http://hdl.handle.net/1721.1/64440
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Motives, Quantum Field Theory, and Pseudodifferential Operators : Conference on Motives, Quantum Field Theory, and Pseudodifferential Operators, June 2-13, 2008, Boston University, Boston, Massachusetts, Clay Mathematics Proceedings Volume 12
Publisher
Clay Mathematics Institute
Citation
Albin, Pierre and Richard Melrose. "Fredholm realizations of elliptic symbols on manifolds with boundary II: fibered boundary." in Motives, quantum field theory, and pseudodifferential operators : Conference on Motives, Quantum Field Theory, and Pseudodifferential Operators, June 2-13, 2008, Boston University, Boston, Massachusetts, (Clay Mathematics Proceedings Volume 12)
Version: Final published version
ISBN
9780821851999

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