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Indefinite Kasparov modules and pseudo-Riemannian manifolds

Journal Article


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Abstract


  • We present a definition of indefinite Kasparov modules, a generalisation of unbounded Kasparov modules modelling non-symmetric and non-elliptic (e.g. hyperbolic) operators. Our main theorem shows that to each indefinite Kasparov module we can associate a pair of (genuine) Kasparov modules, and that this process is reversible. We present three examples of our framework: the Dirac operator on a pseudo-Riemannian spin manifold (i.e. a manifold with an indefinite metric); the harmonic oscillator; and the construction via the Kasparov product of an indefinite spectral triple from a family of spectral triples. This last construction corresponds to a foliation of a globally hyperbolic spacetime by spacelike hypersurfaces.

Publication Date


  • 2016

Citation


  • van den Dungen, K. & Rennie, A. (2016). Indefinite Kasparov modules and pseudo-Riemannian manifolds. Annales Henri Poincare, 17 (11), 3255-3286.

Scopus Eid


  • 2-s2.0-84961615444

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=7048&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6018

Has Global Citation Frequency


Number Of Pages


  • 31

Start Page


  • 3255

End Page


  • 3286

Volume


  • 17

Issue


  • 11

Place Of Publication


  • Switzerland

Abstract


  • We present a definition of indefinite Kasparov modules, a generalisation of unbounded Kasparov modules modelling non-symmetric and non-elliptic (e.g. hyperbolic) operators. Our main theorem shows that to each indefinite Kasparov module we can associate a pair of (genuine) Kasparov modules, and that this process is reversible. We present three examples of our framework: the Dirac operator on a pseudo-Riemannian spin manifold (i.e. a manifold with an indefinite metric); the harmonic oscillator; and the construction via the Kasparov product of an indefinite spectral triple from a family of spectral triples. This last construction corresponds to a foliation of a globally hyperbolic spacetime by spacelike hypersurfaces.

Publication Date


  • 2016

Citation


  • van den Dungen, K. & Rennie, A. (2016). Indefinite Kasparov modules and pseudo-Riemannian manifolds. Annales Henri Poincare, 17 (11), 3255-3286.

Scopus Eid


  • 2-s2.0-84961615444

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=7048&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6018

Has Global Citation Frequency


Number Of Pages


  • 31

Start Page


  • 3255

End Page


  • 3286

Volume


  • 17

Issue


  • 11

Place Of Publication


  • Switzerland