Index in K-Theory for Families of Fibred Cusp Operators |
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| Institution: | (1) Department of Mathematics, Massachusetts Institute of Technology, MA, USA;(2) Department of Mathematics, State University of New York, Stony Brook, NY 11794-3651, USA |
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| Abstract: | A families index theorem in K-theory is given for the setting of Atiyah, Patodi, and Singer of a family of Dirac operators with spectral boundary condition.
This result is deduced from such a K-theory index theorem for the calculus of cusp, or more generally fibred-cusp, pseudodifferential operators on the fibres
(with boundary) of a fibration; a version of Poincaré duality is also shown in this setting, identifying the stable Fredholm
families with elements of a bivariant K-group.
(Received: February 2006) |
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| Keywords: | fibred cusp operators K-theory index Poincaré duality |
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