Index in K-theory for families of fibred cusp operators

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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.
64 pages, corrected typos

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Differential Geometry, K-Theory and Homology, 58J40 (Primary) 19K56, 19K35 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/102144

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0507590
 http://arxiv.org/abs/math/0507590

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arXiv