Fredholm realizations of elliptic symbols on manifolds with boundary II: fibered boundary
Name
melrose Clay Math Proc 12 2010_unlocked.pdf
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556.76 KB
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Author(s)
Albin, Pierre
Melrose, Richard B.
Date Issued
January 2010
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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http://www.claymath.org/publications/Motives_Quantum/
