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Structure of Malicious Singularities

M. Heller·Z. Odrzygozdz·L. Pysiak·W. Sasin
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Abstract

We investigate spacetimes with their singular boundaries as noncommutative spaces. Such a space is defined by a noncommutative algebra on a transformation groupoid $Γ= E \times G$, where $E$ is the total space of the frame bundle over spacetime with its singular boundary, and $G$ its structural group. There is a bijective correspondence between unitary representations of the groupoid $Γ$ and the systems of imprimitivity of the group $G$. This allows us to apply the Mackey theorem, and deduce from it some information concerning singular fibres of the groupoid. A subgroup $K$ of $G$, from which -- according to the Mackey theorem -- the representation is induced to the whole of $G$, can be regarded as measuring the "richness" of the singularity structure.

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M. Heller, Z. Odrzygozdz, L. Pysiak, W. Sasin. 2002-10-29. Structure of Malicious Singularities. https://doi.org/10.1023/a%3A1024429613783

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