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On the bundle of principal connections and the stability of b-incompleteness of manifolds

Published online by Cambridge University Press:  24 October 2008

D. Canarutto  and
C. T. J. Dodson
D. Canarutto
Affiliation:
Applied Mathematics Institute‘G. Sansone’, University of Florence
C. T. J. Dodson
Affiliation:
Department of Mathematics, University of Lancaster
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Abstract

We make use of the universal connection on the bundle of principal connections; the bundle structure is governed by the action of the group on the first jet bundle. Each section determines a connection in the principal bundle, which in the case of the frame bundle allows a metric completion projecting onto the corresponding b-completion. It is shown that b-incompleteness of the base manifold is stable under perturbations of the chosen section. Hence, for instance, for (pseudo) Riemannian manifolds including spacetimes, b-incompleteness is a stable condition under conformal deformations of the metric. This reinforces the belief that general relativistic singularities cannot be removed by quantization.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 1 , July 1985 , pp. 51 - 59
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

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