Index in K-theory for families of fibred cusp operators

Details Index in K-theory for families of fibred cusp operators Index in K-theory for families of fibred cusp operators

2005-07-28

arxiv.org/abs/math/0507590v2

Mathematics

Differential Geometry

64 pages, corrected typos

Scientific paper

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 Poincare duality is also shown in this setting, identifying the stable Fredholm families with elements of a bivariant K-group.

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