## Abstract

What it means for (relative) sheaf cohomology classes to have a pole of a given order on a surface S in twistor space will be defined and that they can be described in terms of some formal neighborhood sheaves will be shown. In space-time, S corresponds to a foliation by alpha-surfaces and the filtration of cohomology gives a filtration on the fields that extends the idea of being algebraically special along the foliation. This idea is also used for the case of the "double-valued" congruence associated with a world line, in which case the filtration applied to soruced fields is essentially a multipole expansion. In the case of curved space-times, it will be shown that if a certain curvature condition holds, then the space of leaves of a foliation by alpha surfaces has an ambient twistor space defined to first order, and we relate this to an extended version of Robinson's theorem.

Original language | English |
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Pages (from-to) | 1465-1469 |

Number of pages | 5 |

Journal | Journal of mathematical physics |

Volume | 32 |

Issue number | 6 |

Publication status | Published - Jun 1991 |

## Keywords

- FIELDS