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LORENTZIAN GEOMETRY AND PHYSICS IN KASPAROV’S THEORY

Part of: Global differential geometry Classical field theories Infinite-dimensional manifolds $K$-theory and operator algebras

Published online by Cambridge University Press:  21 January 2016

KOEN VAN DEN DUNGEN
KOEN VAN DEN DUNGEN*
Affiliation:
Scuola Internazionale Superiore di Studi Avanzati, SISSA, via Bonomea 265, 34136 Trieste, Italy email [email protected]
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Abstract

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Keywords

Lorentzian geometrygauge theoryKasparov’s theoryspectral triples

MSC classification

Primary: 19K35: Kasparov theory ($KK$-theory)
Secondary: 53C50: Lorentz manifolds, manifolds with indefinite metrics 58B34: Noncommutative geometry (à la Connes) 70S15: Yang-Mills and other gauge theories
Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 2 , April 2016 , pp. 340 - 341
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

Boeijink, J. and van den Dungen, K., ‘On globally non-trivial almost-commutative manifolds’, J. Math. Phys. 55(10) 103508 (2014).Google Scholar
Baaj, S. and Julg, P., ‘Théorie bivariante de Kasparov et opérateurs non bornés dans les C ∗ -modules hilbertiens’, C. R. Acad. Sci. Paris Ser. I Math. 296 (1983), 875–878.Google Scholar
Connes, A., Noncommutative Geometry (Academic Press, San Diego, CA, 1994).Google Scholar
van den Dungen, K., Paschke, M. and Rennie, A., ‘Pseudo-Riemannian spectral triples and the harmonic oscillator’, J. Geom. Phys. 73 (2013), 37–55.Google Scholar
van den Dungen, K. and Rennie, A., ‘Indefinite Kasparov modules and pseudo-Riemannian manifolds’, arXiv:1503.06916 (2015).Google Scholar
van den Dungen, K., ‘Krein spectral triples and the fermionic action’, arXiv:1505.01939 (2015).Google Scholar
Kasparov, G. G., ‘The operator K-functor and extensions of C ∗ -algebras’, Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980), 571–636.Google Scholar